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Insurance as AI Risk Infrastructure: A Generative-Agent Simulation of AI Adoption
Yixuan Yuan, Dedai Wei, Chudong Qian, Jielin Feng, Ziyue Lin, Yuheng Zhao, He Cao, Erasmo Purificato, Xinwu Ye
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 96%
Last extracted: 8/18/2026, 4:09:11 AM
Summary
This paper introduces a socio-economic framework proposing insurance as a risk infrastructure to facilitate AI adoption by enterprises. The authors develop an LLM-driven Agent-Based Social Simulation (LABSS) system to model heterogeneous firm behaviors, including AI adoption, renewal, and insurance purchasing decisions under bounded rationality. The simulation demonstrates that providing insurance coverage for residual AI operational losses reduces firm-level financial exposure, decreases bankruptcy rates, and accelerates aggregate AI adoption compared to scenarios without insurance.
Entities (10)
Relation Signals (7)
Jielin Feng → affiliatedwith → Fudan University
confidence 99% · Jielin Feng Affiliation: Fudan University
Yixuan Yuan → affiliatedwith → University of Macau
confidence 99% · Yixuan Yuan Affiliation: University of Macau
Xinwu Ye → affiliatedwith → The University of Hong Kong
confidence 99% · Xinwu Ye... Affiliation: The University of Hong Kong
Insurance → mitigates → AI operational risk
confidence 96% · It transfers and pools residual AI operational risk... converting open-ended firm exposure into priced protection
LABSS → uses → Qwen3-8b
confidence 95% · The LLM decision layer uses Qwen3-8B [29] for firm decisions and bilateral negotiations
LABSS → uses → AutoCLAW
confidence 94% · AutoCLAW [32] generates firm-level evidence on AI operational risk... Across the full simulation, 68,058 task executions are summarized
Insurance → increases → AI adoption
confidence 93% · Our analysis demonstrates that the proposed insurance framework reduces firm-level financial exposure, thereby accelerating the aggregate adoption of AI tools
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Abstract
Abstract:The rapid evolution of artificial intelligence (AI) tools has demonstrated immense potential to enhance societal well-being and operational efficiency. However, the inherent unreliability and uncertain operational consequences of modern AI systems, typified by large language models (LLMs), have created a significant barrier to enterprise adoption. Many enterprises remain hesitant to integrate these tools deeply into their workflows due to concerns about unpredictable losses and liability exposure. While existing technical safeguards primarily seek to reduce the likelihood or severity of AI-enabled workflow failures, they do not by themselves provide ex post financial protection when residual pecuniary tail losses materialize. In this paper, we introduce a socio-economic framework that complements these safeguards by transferring and absorbing the residual financial consequences of AI adoption through insurance. To evaluate this framework, we develop an LLM-driven agent-based social simulation (LABSS) system. We assess the behavioral validity of the simulation using established economic and sociological theories. Our analysis demonstrates that the proposed insurance framework reduces firm-level financial exposure, thereby accelerating the aggregate adoption of AI tools and improving firm solvency and aggregate capital.
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- Source: https://arxiv.org/abs/2608.15181v1
- Canonical: https://arxiv.org/abs/2608.15181v1
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Insurance as AI Risk Infrastructure: A Generative-Agent Simulation of AI Adoption Yixuan Yuan Affiliation: University of Macau Dedai Wei Affiliation: University of Macau Chudong Qian Affiliation: University of Macau Jielin Feng Affiliation: Fudan University Ziyue Lin Affiliation: Fudan University Yuheng Zhao Affiliation: Fudan University He Cao Affiliation: Immunocan AI Erasmo Purificato Affiliation: European Commission Xinwu Ye Corresponding author: *: Corresponding author. Email: xinwuye43@connect.hku.hk Affiliation: The University of Hong Kong Abstract The rapid evolution of artificial intelligence (AI) tools has demonstrated immense potential to enhance societal well-being and operational efficiency. However, the inherent unreliability and uncertain operational consequences of modern AI systems, typified by large language models (LLMs), have created a significant barrier to enterprise adoption. Many enterprises remain hesitant to integrate these tools deeply into their workflows due to concerns about unpredictable losses and liability exposure. While existing technical safeguards primarily seek to reduce the likelihood or severity of AI-enabled workflow failures, they do not by themselves provide ex post financial protection when residual pecuniary tail losses materialize. In this paper, we introduce a socio-economic framework that complements these safeguards by transferring and absorbing the residual financial consequences of AI adoption through insurance. To evaluate this framework, we develop an LLM-driven agent-based social simulation (LABSS) system. We assess the behavioral validity of the simulation using established economic and sociological theories. Our analysis demonstrates that the proposed insurance framework reduces firm-level financial exposure, thereby accelerating the aggregate adoption of AI tools and improving firm solvency and aggregate capital. keywordsAgent-based social simulation, AI adoption, AI governance, AI risk insurance, generative agents, operational risk. 1 Introduction Figure 1: Motivation. (a) The aggregate social benefit of AI adoption decomposes into heterogeneous firm-level value trajectories, with some firms bearing concentrated tail losses. (b) Existing safeguards reduce failure likelihood but cannot compensate realized losses. (c) Insurance pools premiums to compensate affected firms. AI has emerged as a transformative force in the modern economy, offering unprecedented opportunities to optimize operational workflows and elevate societal standards across diverse sectors [1, 2], while the integration of these systems into critical business infrastructure is hindered by their inherent unreliability [3, 4]. A significant dichotomy exists between the potential for aggregate social benefit and the concentrated, potentially catastrophic losses borne by individual firms [2, 5]. At the macro level, broader AI adoption can generate increasing productivity benefits over time. In contrast, individual enterprises may remain deterred by the threat of sudden and potentially ruinous operational losses (Fig. 1(a)) [6]. Recent incidents involving OpenClaw illustrate how failures of AI systems can translate into concrete firm-level operational exposure. When granted access to email accounts and local workspaces, autonomous agents have deleted messages without authorization and overwritten customized workspace files without adequate warning or backup [7, 8]. These incidents show that AI systems acting directly on business processes can cause not only inaccurate outputs but also data loss and workflow disruption. When such residual downside remains open-ended, expected productivity gains need not translate into adoption. AI adoption is often framed primarily as a function of model capability [9], implying that improvements in accuracy and reliability should naturally encourage integration. However, enterprise adoption also depends on whether firms can absorb the operational losses that remain when AI systems fail. Technical safeguards can improve model performance, interpretability, and auditability, while governance regimes based on risk classification, auditing, transparency, and accountability define how AI systems should be built, monitored, and used (Fig. 1(b)) [10, 11, 12]. These measures reduce deployment risk, but they do not provide a buffer when a compliant AI system still causes firm-level operational losses. We therefore introduce insurance as a market-based layer within AI governance. It transfers and pools residual AI operational risk (Fig. 1(c)), converting open-ended firm exposure into priced protection with deductibles, coverage limits, and claim settlement. This layer complements technical safeguards and governance mechanisms for fairness and accountability by enabling ex post financial redress for covered pecuniary harm borne by deploying firms and, through liability coverage, by affected third parties [5]. To evaluate the proposed insurance framework, we develop an LLM-driven agent-based social simulation (LABSS) in which heterogeneous firms make AI adoption, renewal, and insurance decisions under bounded information and evolving market conditions [13, 14, 15]. Within the simulated market, firms integrate market signals, financial and contract states, peer behavior, and accumulated risk experience to form context-dependent decisions. The behavioral design is informed by established economic and sociological mechanisms, including informational-cascade pressure [16], path dependence in technology choice [17], and prospect-theoretic sensitivity to downside risk [18]. We assess the behavioral plausibility of the resulting simulation through formal diagnostics of bounded attention, peer diffusion, contractual inertia, and firm heterogeneity, together with path-level tests of diffusion dynamics, cross-sectional sorting, and contract sensitivity. Together, these evaluations connect heterogeneous firm-level decision processes with the aggregate dynamics of AI adoption, insurance participation, and market adjustment. Within the 300-day simulation, we examine how market outcomes change when firms facing the same underlying AI-risk realizations gain access to insurance for part of the resulting financial losses. Final AI adoption reaches 84.38%, compared with 74.97% without insurance, while the average number of bankrupt firms declines from 4.33 to 1.33 and aggregate capital is higher at the end of the simulation. The insurance-enabled market also exhibits longer vendor commitments and narrower cross-industry adoption gaps. Insurance provides timely compensation for severe AI-related losses through a shared risk pool, reducing firms’ financial burden and dampening panic transmission. In summary, this paper makes the following key contributions: • Proposal of a socio-economic AI risk hedging framework: We introduce an interdisciplinary framework that utilizes financial instruments to hedge against stochastic AI risks. • Development of the LABSS system: We develop an LLM-driven agent-based simulation of heterogeneous firm decisions and validate its behavioral plausibility through theory-grounded mechanism diagnostics and path-level tests. • Identification of emergent social phenomena: Through simulation, we find that insurance increases AI adoption and aggregate capital, reduces bankruptcies, supports longer vendor commitments and cross-industry convergence, and dampens panic transmission. 2 Related Work LLM-Driven Agent-Based Social Simulation Agent-based social simulation has long been used to examine how collective patterns emerge from heterogeneous agents, local interactions, and bounded information [19, 20]. Traditional agent-based models typically represent individual decisions through explicit rules or probabilistic heuristics, whereas recent studies incorporate large language models as cognitive components that can interpret context, maintain memory, and generate adaptive actions [15, 13, 14, 21]. LLM-driven simulations have since been applied to social interaction and network formation [22, 14], epidemic response and opinion dynamics [23], and macroeconomic and social-media systems [24, 25]. Together, these studies demonstrate the potential of LLM agents for modeling heterogeneous, context-dependent behavior and emergent collective dynamics. AI Governance AI governance research addresses risks arising from uncertainty, opacity, and harmful outcomes through both technical and institutional approaches. Technical work emphasizes model trustworthiness through interpretability, transparency, robustness, and auditability [3, 4, 12, 26], while broader governance frameworks distribute responsibilities across firms, regulators, developers, and users and emphasize fairness, human oversight, and stakeholder participation [10, 11, 27]. Related adoption studies further show that organizational trust, perceived controllability, and uncertainty about operational consequences shape firms’ willingness to deploy AI systems [9]. 3 Method We propose a risk-hedging framework that introduces financial instruments into society to mitigate the risks of AI adoption. To validate this framework, we employ insurance as the concrete realization of the financial hedging instrument and construct a LABSS system. Specifically, we test the hypothesis that empowering firms to financially hedge against AI risk accelerates AI diffusion and enhances overall productivity in the simulation system. The framework integrates macro-environmental factors with micro-behavioral agents (Fig. 2). This configuration ensures that the aggregate diffusion of AI emerges directly from the continuous feedback loop between top-down institutional constraints and bottom-up entity choices. Figure 2: Overview. The system integrates macro-environmental uncertainty with micro-cognitive decision-making, orchestrating a lifecycle from signal processing to bilateral negotiation. 3.1 Macro-Environmental Architecture The macro-environmental architecture organizes the 300-day simulation into 100 structured interaction rounds (Fig. 3). The ecosystem contains three agent categories: buyer firms seeking productivity gains, AI vendors supplying technology services, and insurance institutions comprising four private insurers and a residual backstop facility. Each round governs how uncertainty is realized, information is disseminated, decisions are formed, and contracts are settled through six sequential phases. Phase 1: Market-state update. At the beginning of each interaction round, the environment carries forward the outcomes of the preceding round and refreshes the state variables available for current decisions. Expired AI and insurance contracts are removed, active policy counts are recomputed, and aggregate and network-local adoption, insurance coverage, panic, and recent claim rates are updated. Insurer capital and active exposures jointly determine each insurer’s solvency regime, underwriting availability, and remaining capacity. Industry risk snapshots are constructed exclusively from records observed before the current round, preserving the temporal boundary between available information and contemporaneous outcomes. Phase 2: Market publishing and information release. The updated market state is then translated into observable signals. AI vendors publish service profiles covering price, expected performance, reputation, and targeted sectors, while insurers announce coverage availability, indicative policy conditions, and prevailing underwriting regimes. The environment also releases public and network-mediated information derived from previously realized adoption decisions, operational incidents, claims, firm exits, and market panic. Together, these signals define the observable market information environment for the current interaction round. Operational incidents occurring within the current round remain unobserved until the outcome-realization stage. Phase 3: Attention filtering and the endogenous visible set. Constrained by finite attention, the environment constructs a buyer-specific consideration set containing up to three vendors through two complementary sampling channels. One slot is drawn uniformly from the full vendor pool, ensuring a non-zero discovery probability for every vendor. The remaining slots are sampled without replacement with conditional probability piv(k)=mvaiv(b+rv)∑u∈ℛi(k)muaiu(b+ru)p_iv^(k)= m_va_iv(b+r_v) _u _i^(k)m_ua_iu(b+r_u), where ℛi(k)R_i^(k) is the remaining vendor pool, mvm_v, aiva_iv, and rvr_v denote marketing exposure, sector affinity, and reputation, respectively, and b=0.5b=0.5 is the baseline visibility term. The resulting visible set defines the information boundary for the subsequent decision phase. Phase 4: Action proposals under contractual constraints. Conditional on the visible set, firms formulate action plans regarding AI adoption and insurance hedging. These decisions are strictly gated by contract maturities, where active terms enforce continuity while expiration windows authorize vendor switching or coverage adjustments. Validated intents are subsequently forwarded to the negotiation stage. Figure 3: The Macro-Environmental Interaction Cycle. This diagram illustrates the cyclical flow of information and capital between the environment, AI vendors, insurers, and buyer firms, governing the transition from signal emission to contract realization. Phase 5: Negotiation and contract formation. Proposals are converted into binding commitments through negotiation. Firms bargain for service terms with AI vendors, while insurance requests undergo underwriting subject to insurer constraints. Successful outcomes crystallize into formalized contracts specifying payment structures and coverage clauses, whereas failed negotiations revert the firm to its status quo. These contracts define the governing rules for the subsequent realization of financial outcomes and claim assessments. Phase 6: Settlement, outcome realization, and claims. The cycle concludes with financial settlement. Let Πit0=Airit0 ^0_it=A_ir^0_it denote baseline operating profit, where rit0r^0_it already incorporates the idiosyncratic operating shock. The action-risk mapping produces a monetary AI gain GitAIG^AI_it and a monetary operational loss ℓit _it, both of which are zero without active AI exposure. The operating cash contribution before contractual transfers and indemnity is ΔCashitop=Πit0+GitAI−ℓit ^op_it= ^0_it+G^AI_it- _it. Vendor fees, premiums, refunds, and paid claims enter separately in the complete cash transition reported in Appendix A. Regarding risk transfer, verified claims result in indemnity payouts subject to policy limits and insurer solvency, effectively updating the market information state for the subsequent period. 3.2 Micro-Behavioral Dynamics Figure 4: The AAD Framework. The micro-level cognitive process where firms filter signals (Attention), evaluate risks (Assessment), and execute strategies (Decision). At the micro level, we model firm behavior through the lens of corporate behavioral finance and organizational theory. Specifically, we introduce an Attention-Assessment-Decision (AAD) framework to structure the boundedly rational decision process of heterogeneous firms (Fig. 4). Attention Attention governs the availability of market information. Rather than assuming full omniscience, firms observe a limited and time-varying consideration set comprising visible AI advertisements, insurance quotes, and salient network signals. This exposure is strictly bounded by finite cognitive capacity, ensuring that firms process only a fraction of available opportunities. Consistent with endogenous consideration models, this mechanism acts as the primary filter determining which options enter subsequent evaluation [28]. Assessment Assessment translates the filtered attention set into perceived risk and strategic intent. Rather than following deterministic profit maximization, firms combine internal factors such as capital solvency and behavioral inertia with external network signals regarding market volatility. Consistent with corporate behavioral finance, they form discrete action tendencies ranging from status quo maintenance to AI termination or risk transfer. Decision Decision translates the preferences based on the assessment into binding operational commitments. Firms choose among operating without AI, utilizing AI independently, or combining AI adoption with insurance hedging. These choices are conditional on negotiation success and market availability and update the firms’ technological and contractual states for subsequent periods. 3.3 Short and long horizon memory mechanism The AAD process incorporates a two-horizon memory mechanism. The short-horizon state captures current contract conditions, recent claims, industry risk, and local network conditions relevant to attention and feasibility checks, whereas the long-horizon state summarizes accumulated material risk, realized loss, and claimable loss through exponential carryover. Uninsured claimable losses reinforce the loss and claimable-loss memories, while paid claims attenuate them; panic is tracked separately. At each firm decision, the LLM receives these structured states without retaining an unbounded conversation history. 3.4 Experimental Setup To evaluate the proposed insurance mechanism, we compare simulations of an AI service market with and without insurance. The LLM decision layer uses Qwen3-8B [29] for firm decisions and bilateral negotiations, with the model interface and inference settings reported in Appendix B. The insurance arm permits policy purchase, premium payment, and indemnity for eligible AI operational losses, whereas these channels are disabled in the no-insurance arm. We repeat the comparison under three random seeds, yielding three matched replications in which the two arms otherwise share identical settings and random initialization. The details are reported in Appendix A. Firm population and industries The simulated economy contains 300 buyer firms distributed across 11 GICS-aligned sectors [30]. Firm-size heterogeneity captures differences in liquidity and risk-bearing capacity, while the profiles also vary in AI-related organizational traits and sensitivity to risk and peer influence. The population construction, profile specification, and descriptive distributions are reported in Appendix J. Each replication spans 300 days and consists of 100 interaction rounds covering firm decisions, contract updates, operational-risk realization, and financial settlement. Reported results are aggregated across the three paired replications. AI vendor market The AI market contains four stylized vendors representing distinct strategic positions [31]. Alpha is stability-oriented, Beta is productivity-oriented, Gamma is sector-specialized, and Delta is a low-cost generalist. Their profiles differ in subscription fee, productivity lift, operational risk multiplier, reputation, marketing weight, and target sectors, with the exact parameterization reported in Table 4. Firms do not observe the full vendor menu in every operational cycle; the consideration set contains at most three vendors, with one sampled uniformly for exploration and the remaining slots filled by weighted sampling based on marketing weight, sector affinity, and reputation. The visibility rule and its parameter values are reported in Table 3. Vendor contracts create lock-in until renewal or cancellation conditions reopen the choice window. Insurance market The insurance market contains four private insurers and one residual backstop facility. The four private insurers represent diversified commercial, SME-oriented mutual commercial, digital commercial, and specialty technology underwriting archetypes. Their profiles differ across capitalization and capacity, underwriting and pricing, contract design, solvency controls, and sector focus, with exact settings reported in Table 5. The residual backstop facility is retained as a policy backstop rather than as an ordinary competitive insurer. In the no-insurance arm, all insurance purchase, premium, active policy, and claim settlement channels are disabled. Risk-based premiums, deductibles, and coinsurance consequently vary across contracts, whereas moral hazard and adverse selection are held constant. AutoCLAW risk data At each operational update, AutoCLAW [32] generates firm-level evidence on AI operational risk through sector-specific enterprise tasks covering document generation and revision, directory auditing and file cleanup, constrained summarization, record maintenance, email drafting, and CSV updates. An autonomous AI agent executes each task in a sandboxed workspace. A deterministic verifier evaluates task completion and policy violations, after which a rule-based risk-mapping procedure converts the evidence into incident indicators, severity scores, direct and total losses, and risk scores. Across the full simulation, 68,058 task executions are summarized into 30,000 records covering 300 firms over 100 operational updates. 4 Experimental Validation Experimental validation evaluates both the theoretical grounding of the model design and the empirical realism of the dynamics it generates. Mechanism diagnostics connect the specified decision mechanisms to established theories of bounded attention, social influence, contractual inertia, and organizational heterogeneity, and examine whether their expected signatures are present in firm-level records. Path-level validation compares the resulting adoption and coverage trajectories with documented empirical regularities in technology diffusion, cross-sectional sorting, and contract choice. A matched rule-based ABM benchmark and parameter sensitivity analysis provide complementary evidence on decision-model dependence and parameter robustness, respectively, with full results reported in Appendices D and E. 4.1 Mechanism Diagnostics Mechanism diagnostics examine how the information, contract, and behavioral structure of the simulation is reflected in firm decisions and subsequent network dynamics. The tests use structured decision records, contract events, and parsed adoption scores from the three formal seeds. M1 verifies adherence to the bounded vendor menu, while the expiry-window component of M3 verifies contract timing. M2, incumbent retention in M3, and M4 evaluate how model-generated assessments and choices vary with peer adoption, prior vendor relationships, and heterogeneous firm and industry states. M5 extends the analysis to sectoral propagation by testing whether the configured network affinity is reflected in realized panic co-movement. Table 1 reports the compact statistical verdicts; the definitions and test formulas are stated in the text. M1 tests bounded attention. Let VjsV_js be the number of vendors visible in adoption decision j of seed s, and let NsN_s be the number of such decisions. The full-menu null is V¯s=4 V_s=4 and πs<4=0 _s^<4=0, where V¯s=1Ns∑j=1NsVjs V_s= 1N_s _j=1^N_sV_js and πs<4=1Ns∑j=1NsVjs<4 _s^<4= 1N_s _j=1^N_s1\V_js<4\. In all seeds, firms observe exactly three vendors in every adoption decision, so V¯s=3 V_s=3 and πs<4=1.00 _s^<4=1.00. This rejects the full-menu null and confirms that the recorded choices conform to the bounded consideration set. M2 tests social diffusion in adoption assessment. We estimate Scoreit=α+βPeerAdoptit+γXit+ϵit, [rgb]0,0,0Score_it=α+β PeerAdopt_it+γ X_it+ _it, (1) where ScoreitScore_it is the parsed adoption score, PeerAdoptitPeerAdopt_it is the visible network-neighbor adoption share, and XitX_it includes day, risk-transfer evidence, technology urgency, AI dependence, and inertia. The null is β≤0β≤ 0 against β>0β>0. The estimated peer coefficients are 0.0134, 0.0173, and 0.0267 across the three seeds, all with p<0.001p<0.001, rejecting the no-positive-peer-effect null. M3 tests contractual inertia. For renewal decision RjsR_js, let EjsE_js indicate that the window is opened by contract expiry, AjsA_js denote a renewal action, SjsS_js the selected vendor, and LjsL_js the previous vendor. We compute πsexpiry π^expiry_s =Pr(Ejs=1∣Rjs=1), = (E_js=1 R_js=1), (2) ρsinc ρ^inc_s =Pr(Sjs=Ljs∣Rjs=1,Ajs=1). = (S_js=L_js R_js=1,A_js=1). All renewal decisions are expiry-triggered, and incumbent retention conditional on renewal ranges from 93.68% to 95.88%. The logged contract lifecycle therefore conforms to the renewal gate, while the subsequent vendor choices exhibit strong incumbent persistence. M4 tests whether firm traits and industry indicators explain adoption scores beyond day and seed terms. We compare a restricted model with a full model using F F =(RSSr−RSSf)/(dfr−df)RSSf/df, = (RSS_r-RSS_f)/(df_r-df_f)RSS_f/df_f, (3) Rpartial2 R^2_partial =RSSr−RSSfRSSr, = RSS_r-RSS_fRSS_r, where r and f denote the restricted and full models. Technology urgency and AI dependence enter positively, inertia enters negatively, and the signs are significant in every seed. Adding industry indicators gives F=656.96F=656.96, p<10−300p<10^-300, and partial R2=0.204R^2=0.204, rejecting the homogeneous-firm null. Table 1: Compact mechanism diagnostics before path-level validation. Item Test Statistic Null hypothesis Result Decision M1. Bounded attention Menu-conformance audit V¯s V_s, πs<4π^<4_s H0:V¯s=4H_0: V_s=4, πs<4=0π^<4_s=0 V¯s=3 V_s=3; πs<4=1.00π^<4_s=1.00 Reject H0H_0 M2. Peer diffusion Peer-response regression β β H0:β≤0H_0:β≤ 0 0.0134,0.0173,0.02670.0134,0.0173,0.0267; all p<0.001p<0.001 Reject H0H_0 M3. Contract inertia Renewal-gate and retention audit πsexpiryπ^expiry_s, ρsincρ^inc_s H0H_0: no expiry gate or incumbent retention πsexpiry=1.00π^expiry_s=1.00; ρsinc=0.9368ρ^inc_s=0.9368–0.95880.9588 Reject H0H_0 M4. Heterogeneity Heterogeneity F-test F, partial R2R^2 H0H_0: traits and industry add no fit F=656.96F=656.96; p<10−300p<10^-300; partial R2=0.204R^2=0.204 Reject H0H_0 Collectively, the diagnostics show bounded-menu conformance, peer responsiveness, renewal timing and incumbent persistence, and heterogeneous adoption assessment. M5 then examines whether the configured network structure is reflected in sectoral panic dynamics. Figure 5: Sectoral network diagnostic. Bubble correlation matrix of industry-level mean panic paths over the post-diffusion window. The upper triangle reports insurance, and the lower triangle reports no insurance. Circle area encodes |r||r|, and color encodes the sign. M5. Sectoral network diagnostic. The network assigns stronger exposure among firms in the same industry and weaker exposure across industries. The observable implication is not a homogeneous panic field, but sector-level co-movement that remains structured by industry proximity. We compute pairwise correlations of the 11 GICS industry mean-panic paths over the post-diffusion window. The no-insurance arm has a mean off-diagonal correlation of 0.176, while the insurance arm is near zero at −0.007-0.007. Fig. 5 supports the industry-affinity channel used by the network engine: localized AI losses can synchronize sectoral panic when they remain uninsured, whereas risk transfer dampens that synchronization before it becomes an aggregate sentiment burden. 4.2 Path Level Validation Path-level validation asks whether the audited decision layer generates credible intermediate market trajectories before Section 5 interprets social capital and bankruptcy. The evidence consists of paired cycle-indexed panels from seeds 42, 77, and 202, including AI adoption, insurance coverage, GICS industry, firm size, and quote-level insurance choices. H1 tests whether risk transfer creates a stronger AI adoption path while preserving standard diffusion, sector, and size regularities. H2 tests whether insurance coverage has its own product-market structure, including diffusion, cross-sectional sorting, and quote-level contract sensitivity. Figure 6: Market path composition in the formal insurance arm. Panels (a)–(b) show active AI use by vendor and GICS industry, and panels (c)–(d) show insurance coverage by insurer and GICS industry. Dark lines denote the corresponding aggregate levels. H1a-H1b. Adoption diffusion. The first adoption-path tests ask whether active AI use and cumulative ever-adoption follow diffusion dynamics rather than linear drift. Active use can fall after cancellations, so H1a fits the stock path yt=b+Lu1+exp[−ku(t−tu)]−Ld1+exp[−kd(t−td)]. [rgb]0,0,0y_t=b+ L_u1+ [-k_u(t-t_u)]- L_d1+ [-k_d(t-t_d)]. (4) while cumulative ever-adoption cannot decline, so H1b fits the logistic entry path yt=b+L1+exp[−k(t−t0)]y_t=b+ L1+ [-k(t-t_0)], with derivative benchmark Lkgt(1−gt)Lkg_t(1-g_t) and gt=[1+exp[−k(t−t0)]]−1g_t=[1+ [-k(t-t_0)]]^-1. Within each insurance-arm seed, the candidate form is fitted to the complete 100-update path and compared with a linear path using R2R^2 and ΔAIC=AIClinear−AICcandidate AIC=AIC_linear-AIC_candidate. The reported fit statistics are means over the three path-specific fits. The model-selection null is H0:ΔAIC≤0H_0: AIC≤ 0. Rogers and Bass motivate the S-shaped benchmark [33, 34]. The results reject H0H_0 for H1a and H1b: active AI use has mean R2=0.996R^2=0.996 and mean ΔAIC=476.7 AIC=476.7, while cumulative ever-adoption has mean R2=0.998R^2=0.998, mean ΔAIC=532.1 AIC=532.1, and a first-start peak on days 57 to 69. H1c. Risk-transfer adoption lead. The paired insurance effect is measured by the cycle-T adoption gap, the average cycle-level gap, and the area under the paired gap curve. Define ds,t=ys,ton−ys,toffd_s,t=y^on_s,t-y^off_s,t, d¯s=T−1∑tds,t d_s=T^-1 _td_s,t, AUCs=∑tds,tAUC_s= _td_s,t. Path fits use the complete 100-update record within each formal seed. The paired insurance contrast is evaluated across matched seeds; timing and sorting diagnostics resample complete firm trajectories within seed; and contract sensitivity is evaluated within completed quote sets. For H1c, the paired end-point contrast is tested with td=Sd¯Tsd(ds,T),d¯T=1S∑s=1Sds,T,H0:[ds,T]≤0, [rgb]0,0,0 [rgb]0,0,0t_d= S\, d_Tsd(d_s,T), d_T= 1S _s=1^Sd_s,T, H_0:E[d_s,T]≤ 0, (5) where S=3S=3 paired seeds. The terminal contrast is the inferential quantity, while d¯s d_s and AUCsAUC_s summarize each complete path. Real options and risk-bearing theory predict shorter waiting under risk transfer [35, 36], and the Ghana rainfall-insurance field experiment provides an external analogue for insurance raising risky production investment [37]. The final gaps are (5.92,13.38,8.93)(5.92,13.38,8.93) p, the mean cycle gaps are (26.06,30.05,29.42)(26.06,30.05,29.42) p, and AUCs>0AUC_s>0 in every paired seed. The mean final gap is 9.41 p, with a one-sided paired-seed test of p=0.025p=0.025. H1d. Digital timing. Let τi,s _i,s denote the first operational cycle in which firm i in seed s holds active AI exposure, for each firm with an observed first adoption, and let Δτ=1S∑s=1S(τ¯s,non-digital−τ¯s,digital). [rgb]0,0,0 [rgb]0,0,0 ^τ= 1S _s=1^S ( τ_s,non -digital- τ_s,digital ). (6) H1d, H1e, H2b, and H2c use complete firm trajectories as resampling units, with 300 firms in each formal seed. Within each seed, the relevant digital-sector or size label is permuted across trajectories while preserving the seed-specific group counts and each trajectory’s complete cycle history. For a one-sided statistic T, the permutation probability is pperm=1+∑b=1BT(b)≥TobsB+1,B=1,000. [rgb]0,0,0 [rgb]0,0,0p_perm= 1+ _b=1^B1\! \T^(b)≥ T^obs \B+1, B=1,000. (7) For H1d, T=ΔτT= ^τ. Eurostat AI and ICT-security statistics anchor the expected sector and size directions [38, 39]. Digital firms adopt (9.54,9.67,10.15)(9.54,9.67,10.15) operational updates earlier across the three seeds, giving Δτ=9.79 ^τ=9.79 operational updates and pperm=0.001p_perm=0.001. H1e. AI size order. For the 70 post-diffusion operational cycles +T_+ in each seed, let as,tga^g_s,t denote active AI adoption for firm-size group g∈L,M,Sg∈\L,M,S\ and define πAI=1S∑s=1S1|+|∑t∈+as,tL>as,tM>as,tS. [rgb]0,0,0 [rgb]0,0,0π^AI= 1S _s=1^S 1|T_+| _t _+1\! \a^L_s,t>a^M_s,t>a^S_s,t \. (8) Equation (7) uses T=πAIT=π^AI and H0:πAI≤1/6H_0:π^AI≤ 1/6. The seed-specific order frequencies are (0.757,0.329,0.757)(0.757,0.329,0.757), giving πAI=0.614π^AI=0.614 and pperm=0.001p_perm=0.001. H2a. Insurance product diffusion. H2 first asks whether coverage itself diffuses as a market product. The coverage paths reuse the stock form in Eq. (4) and the logistic entry form defined above, each fitted over the complete 100-update insurance-arm path. The results reject H0H_0 for H2a: final coverage is 82.14% overall and 97.36% among AI adopters; active coverage has mean R2=0.994R^2=0.994, while cumulative first purchase has mean R2=0.998R^2=0.998. H2b-H2c. Coverage sorting by size and sector. Product take-up should also vary across firm types. Let cs,tgc^g_s,t denote group-g insurance coverage in seed s and cycle t. The corresponding size-order frequency and final digital coverage contrast are πIns π^Ins =1S∑s=1S1|+|∑t∈+cLs,t>cMs,t>cSs,t, = 1S _s=1^S 1|T_+| _t _+1\! \c^L_s,t>c^M_s,t>c^S_s,t \, (9) Δcov ^cov =1S∑s=1S(cs,Tdigital−cs,Tnon-digital). = 1S _s=1^S (c^digital_s,T-c^non-digital_s,T ). For H2b, Eq. (7) uses T=πInsT=π^Ins and H0:πIns≤1/6H_0:π^Ins≤ 1/6; for H2c, it uses T=ΔcovT= ^cov and H0:Δcov≤0H_0: ^cov≤ 0. UK cyber-insurance statistics and insurance-demand studies motivate heterogeneous take-up across firms and sectors [40, 41, 42, 43]. The size-order frequencies are (0.829,0.643,0.857)(0.829,0.643,0.857), giving πIns=0.776π^Ins=0.776 and pperm=0.001p_perm=0.001. Final digital coverage exceeds non-digital coverage by (10.17,8.72,10.00)(10.17,8.72,10.00) p across the seeds, giving Δcov=9.63 ^cov=9.63 p and pperm=0.001p_perm=0.001. H2d. Quote choice. The final product-market test asks whether selected policies depend on contract terms rather than random quote exposure. For quote set C, Pr(q∣C)=exp(Xqβ)∑j∈Cexp(Xjβ), [rgb]0,0,0 (q C)= (X_qβ) _j∈ C (X_jβ), (10) where XqX_q contains standardized log premium, coverage ratio, deductible ratio, and log policy limit. Each completed quote set forms one within-set choice problem. The conditional-logit panel contains 2,495 nondegenerate completed quote sets and 8,465 quote alternatives. The null is H0:=H_0: β=0. The likelihood-ratio statistic is LR(4)=5,065.84LR(4)=5,065.84 with p<0.001p<0.001; the estimated coefficients have the predicted directions for log premium (−23.38-23.38), coverage (+1.36+1.36), and deductible (−1.69-1.69). Across all 2,553 completed sets, quote alternatives at or below their within-set median premium have a 51.38% selection rate, compared with 2.97% for alternatives above the median. Fig. 6 provides the composition check for both claims. Adoption is distributed across vendors and industries, and insurance coverage is distributed across insurers and industries, so the paths are not artifacts of a single supplier, insurer, or sector. Table 2 condenses the path-level evidence into the tested item, statistical procedure, null hypothesis, result, and decision. Table 2: Compact path-level validation of intermediate market behavior. Item Test Statistic Null hypothesis Result Decision H1a. Active stock Trajectory model comparison R2R^2, ΔAIC AIC H0:ΔAIC≤0H_0: AIC≤ 0 33 paths ×100× 100 updates; mean R2=0.996R^2=0.996, ΔAIC=476.7 AIC=476.7 Reject H0H_0 H1b. Entry S-curve Trajectory model comparison R2R^2, ΔAIC AIC, peak H0:ΔAIC≤0H_0: AIC≤ 0 33 paths ×100× 100 updates; mean R2=0.998R^2=0.998, ΔAIC=532.1 AIC=532.1; peak days 5757–6969 Reject H0H_0 H1c. Risk-transfer lead Paired seed-endpoint contrast d¯T d_T, AUCsAUC_s, tdt_d H0:[ds,T]≤0H_0:E[d_s,T]≤ 0 33 pairs; d¯T=+9.41 d_T=+9.41 p; AUCs>0AUC_s>0 (3/3)(3/3); p=0.025p=0.025 Reject H0H_0 H1d. Digital timing Within-seed trajectory-label permutation Δτ ^τ, ppermp_perm H0:Δτ≤0H_0: ^τ≤ 0 300300 firms/seed; Δτ=9.79 ^τ=9.79 updates; pperm=0.001p_perm=0.001 Reject H0H_0 H1e. AI size order Within-seed trajectory-label permutation πAIπ^AI, ppermp_perm H0:πAI≤1/6H_0:π^AI≤ 1/6 300300 firms/seed; πAI=0.614π^AI=0.614; pperm=0.001p_perm=0.001 Reject H0H_0 H2a. Product diffusion Coverage trajectory fit Coverage, R2R^2 H0H_0: no product-diffusion structure 33 paths ×100× 100 updates; active R2=0.994R^2=0.994, entry R2=0.998R^2=0.998 Reject H0H_0 H2b. Insurance size order Within-seed trajectory-label permutation πInsπ^Ins, ppermp_perm H0:πIns≤1/6H_0:π^Ins≤ 1/6 300300 firms/seed; πIns=0.776π^Ins=0.776; pperm=0.001p_perm=0.001 Reject H0H_0 H2c. Digital coverage Within-seed trajectory-label permutation Δcov ^cov, ppermp_perm H0:Δcov≤0H_0: ^cov≤ 0 300300 firms/seed; Δcov=9.63 ^cov=9.63 p; pperm=0.001p_perm=0.001 Reject H0H_0 H2d. Quote choice Within-set conditional logit LR(4)LR(4), β H0:=H_0: β=0 2,4952,495 sets, 8,4658,465 quotes; LR=5,065.84LR=5,065.84; p<0.001p<0.001 Reject H0H_0 Taken together, the path tests establish that the counterfactual comparison enters Section 5 with validated intermediate behavior: diffusion shape, paired insurance lead, external sector and size orderings, endogenous insurance take-up, and quote-level contract sensitivity. The same paired runs are then used to evaluate social total capital and bankruptcy as final system outcomes. 5 Insurance as AI Risk Infrastructure In this section, we examine how AI risk insurance affects firms and the broader market. The analysis links the absorption of severe operational losses to firm solvency and aggregate capital, changes in adoption and market behavior, and the functioning of the insurance pool. Taken together, the results show how risk transfer shapes enterprise AI deployment and market stability. 5.1 Outcome Layer: Solvency and Social Capital Figure 7: Bankruptcy dynamics. Cumulative bankruptcy counts by operational cycle in the paired counterfactual. Faint paths show seed-level integer trajectories; bold paths show the three-seed mean. Insurance substantially reduces firm exits caused by severe AI operational losses. The mean cumulative number of bankruptcies declines from 4.33 firms without insurance to 1.33 firms with insurance (Fig. 7). Indemnity payments offset part of eligible losses and ease the resulting cash pressure on affected firms, preventing some severe incidents from leading to bankruptcy. Figure 8: Capital decomposition. The left panel tracks the social total capital index relative to the no-insurance arm and the cumulative reduction in unabsorbed claimable loss. The right panels compare the final capital index and cumulative unabsorbed claimable loss across arms. The broader economic benefit of insurance lies in its ability to preserve aggregate capital by reducing the disruption caused by severe AI-related losses. By the end of the 300-day simulation, the social total capital index rises from 101.85 without insurance to 103.86 with insurance, corresponding to an increase in aggregate capital from 105.6M to 107.7M and a gain of 2.01 index points (Fig. 8). Over the same horizon, cumulative unabsorbed claimable loss declines from 4.64M to 3.08M, leaving firms with 1.55M less residual loss exposure. Together, these results link lower residual loss exposure to stronger operational continuity and higher aggregate capital. 5.2 Market-Adjustment Layer: Adoption, Contracts, and Allocation The second layer asks how the validated adoption shift is produced inside the market. The outcome analysis shows that insurance improves solvency and social capital, while path-level validation shows that adoption and coverage move in the expected direction. We therefore examine three behavioral margins that connect the two: contract horizons, cross-industry diffusion, and vendor allocation. Figure 9: Vendor contract terms. Distribution of term lengths for successfully bound AI vendor contracts, measured in operational updates. Insurance affects not only firms’ willingness to adopt AI but also the duration of their contractual commitments. When insurance is available, the mean vendor-contract term rises from 56.8 to 65.9 operational updates, and the distribution shifts toward longer commitments (Fig. 9). By reducing firms’ financial exposure to severe operational losses, insurance supports longer planning horizons and greater contractual continuity, while contract lengths remain heterogeneous across firms. Figure 10: Diffusion and industry convergence. Aggregate AI adoption and the cross-industry adoption IQR, defined at each three-day observation as the difference between the 75th and 25th percentiles of adoption rates across the 11 GICS industries. Lower IQR indicates stronger convergence. The industry-level results reveal a convergence effect accompanying the expansion of AI adoption. Following the initial divergence generated by asynchronous sectoral entry, adoption dispersion contracts more rapidly when insurance is available (Fig. 10). By the end of the 300-day simulation, the interquartile range across the 11 industry-level adoption rates falls to 10.98% with insurance, compared with 19.48% without insurance. By easing the financial consequences of severe operational losses, insurance lowers adoption barriers in more risk-sensitive industries and allows AI diffusion to extend beyond the leading sectors. This broader participation narrows persistent adoption gaps across industries. Figure 11: Vendor allocation. Final vendor market share, realized tail risk, and average task error in the insurance arm. Vendor allocation under insurance is distributed across providers with distinct risk and performance profiles. Vendors Alpha and Beta hold the largest final market shares while maintaining relatively balanced tail-risk and task-error profiles (Fig. 11). Vendor Delta records the lowest average task error but a higher tail-risk profile and smaller market share, whereas Vendor Gamma combines the highest error and tail risk with a limited share. These differences reflect trade-offs among routine performance, tail exposure, sector fit, and price, leaving adoption distributed across multiple vendor profiles. Figure 12: Sector-specific vendor composition. Final AI vendor composition by industry in the insurance-on arm. The dark grey ring denotes the uninsured share. The sector-level composition provides a disaggregated view of the insurance-enabled AI market. As shown in Fig. 12, industries differ in both vendor allocation and the share of AI adoption accompanied by insurance coverage. These patterns reflect variation in task requirements, vendor specialization, financial capacity, and tolerance for retained operational risk. Thus, broader market participation coexists with sector-specific differences in vendor and coverage choices. 5.3 Risk-Pool Layer: Claims, Capital, and Panic Transmission Figure 13: Insurance risk-pool ledger. Cumulative premiums and cumulative paid claims are reported in millions of dollars. The shaded band denotes the premium-funded buffer between the two cumulative flows, and the vertical bars report paid claims per operational update. The financial capacity of the insurance mechanism is sustained by pooling premiums across firms and over time. By the end of the 300-day simulation, cumulative premiums reach 7.80M and paid claims reach 4.70M, leaving a premium-funded buffer of 3.10M and an aggregate insurer-capital index of 1.10 (Fig. 13). Claim payments occur in concentrated spikes, while premium contributions accumulate steadily. This structure allows the pool to retain capital between loss events and settle severe claims when firm liquidity is most constrained. Figure 14: Panic tail and aggregate burden. The upper panel shows the 95th-percentile panic trajectory and the lower panel the cumulative mean panic burden, both in 10−310^-3 units; shading denotes the no-insurance excess. Insurance also stabilizes firms’ behavioral responses to AI losses by reducing both acute panic and its cumulative persistence. The 95th-percentile panic trajectory peaks at 30.7 ×10−3× 10^-3 without insurance, compared with 6.7 ×10−3× 10^-3 with insurance, while cumulative mean panic burden over the 300-day simulation declines from 203.2 ×10−3× 10^-3 to 36.3 ×10−3× 10^-3 (Fig. 14). By relieving liquidity pressure following severe incidents, claim payments limit the persistence of adverse experience in firm memory and peer signals. This weakens the feedback from realized losses to subsequent adoption and renewal decisions. 6 Conclusion The study examines whether market-based risk transfer can support enterprise AI adoption when AI failures create operational tail losses. In a paired three-seed simulation with identical firms, vendors, AutoCLAW risk inputs, and decision rules, making AI risk insurance available raises final AI adoption from 74.97% to 84.38%, increases the social total capital index from 101.85 to 103.86, and reduces bankruptcies from 4.33 to 1.33 firms on average. 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Vickery, “Barriers to household risk management: Evidence from India,” American Economic Journal: Applied Economics, vol. 5, no. 1, p. 104–135, 2013. [42] X. Giné and D. Yang, “Insurance, credit, and technology adoption: Field experimental evidence from Malawi,” Journal of development Economics, vol. 89, no. 1, p. 1–11, 2009. [43] National Association of Insurance Commissioners, “Report on the cybersecurity insurance market,” https://content.naic.org/sites/default/files/inline-files/2025_Cybersecurity_Insurance%20Report.pdf, 2025, accessed 24 June 2026. Appendix A Formal Configuration, Risk Mapping, and Accounting The appendix is organized as an audit chain. Appendix A fixes the economic configuration, action-risk map, insurance pricing, settlement order, and accounting identities. Appendix B records the LLM interface, bounded state, decision controls, parser, and retained audit trail. The following appendices report representative decision traces, the matched rule-based ABM, parameter sensitivity, the AutoCLAW task substrate, and supporting environment documentation. A.1 Formal Simulation and Market Parameters The formal configuration is fixed before the paired counterfactuals are compared. Table 3 reports the scalar settings that govern the simulation clock, balance sheets, network, event mapping, memory, panic, contracts, and bargaining. Table 7 separately identifies the parameters varied in the one-factor sensitivity analysis. A machine-readable configuration snapshot and the initialized firm population accompany each run in the reproducibility package. The task-to-loss map retains the cross-task ordering and heterogeneity of the update-aligned AutoCLAW evidence stream while rescaling realized losses to firm balance sheets. Behavioral and market coefficients operate on normalized state variables, and Table 7 reports the local ranges used to evaluate dependence on each selected mechanism intensity. Table 3: Formal runtime and state-transition parameters. The simulation advances once every three calendar days. Values are shared by the insurance-on and insurance-off arms unless the insurance market itself is disabled. Parameter block Exact formal setting Population and horizon 300 buyer firms, comprising 197 small, 69 medium, and 34 large firms; 11 sectors; a 300-calendar-day horizon with one operational update every three days; paired seeds 42, 77, and 202; four AI vendors; four private insurers and one residual backstop. Sector allocation Communication services 28; consumer discretionary 36; consumer staples 26; energy 19; financials 32; health care 24; industrials 31; information technology 37; materials 19; real estate 24; utilities 24. Firm cash and returns Initial cash =0.30Ai=0.30A_i; traditional return mean =−0.00008=-0.00008, standard deviation =0.0035=0.0035, lower cap =−0.025=-0.025, and upper cap =0.010=0.010; AI gain scale =0.078=0.078; AI gain risk drag =0.70=0.70. Peer-information network 12 same-sector and 4 cross-sector neighbors, minimum degree 10, and recent-claim window 7 operational updates. Vendor attention The visible set contains at most three vendors. One slot is sampled uniformly from the full vendor pool, and the remaining slots are sampled without replacement using the Phase 3 visibility probability. Sector affinity equals 1.00 for a targeted sector, 0.75 for an all-sector vendor, and 0.35 otherwise; baseline visibility is b=0.50b=0.50. A numerical weight floor of 0.01 is applied in the implementation and is nonbinding under the formal vendor profiles. Event and loss mapping Risk-score floor =0.02=0.02; loss realization r=0.70r=0.70; action-loss scale s=3.35s=3.35; catastrophic threshold =0.25=0.25; tail multiplier coefficient =12.0=12.0; material-loss ratio =0.0015=0.0015; claimable-loss ratio =0.0030=0.0030; minimum claimable-loss ratio =0.0012=0.0012; material-event score threshold =0.46=0.46; claimable-event score threshold =0.54=0.54. Experience memory Risk, loss, and claimable-memory decay =(0.86,0.88,0.90)=(0.86,0.88,0.90); uninsured-loss and uninsured-claimable boosts =(0.16,0.10)=(0.16,0.10); paid-claim relief to loss and claimable memory =(0.35,0.18)=(0.35,0.18). Panic state Persistence =0.82=0.82; calm decay =0.02=0.02; material-event, claimable-event, paid-claim, and uninsured-claimable weights =(0.18,0.32,0.08,0.58)=(0.18,0.32,0.08,0.58); indemnity relief =0.34=0.34; insurance reassurance =0.12=0.12; severity =0.08=0.08; neighbor and own-event weights =(0.35,0.30)=(0.35,0.30). Contract lifecycle Vendor term 14–120 operational updates; shared insurance lifecycle range 1–120 updates, with the formal firm-decision menu imposing the stricter 1–90 update range and the remaining-AI-term cap; initial adoption trial cap 60 updates unless the decision-score margin is at least 0.08; abandonment and failed-renewal re-entry cooldown 7 updates; minimum remaining term for abandonment 7 updates; claim cooldown 1 update. Vendor refund cap =0.70=0.70, refund penalty =0.10=0.10, and nonlinearity =2.0=2.0; insurance refund penalty =0.06=0.06. Bargaining controls Default vendor and insurance limits 10 rounds; minimum vendor and insurance rounds =(3,4)=(3,4); hard cap 30 rounds; vendor and insurance cash-share ceilings =(0.055,0.13)=(0.055,0.13); vendor acceptance slack =0.015=0.015; insurance floor ratio =0.84=0.84. The four vendor profiles implement controlled product differentiation across price, productivity, operational risk, reputation, market visibility, and sector scope. Alpha combines the highest fee with the lowest risk multiplier and highest reputation; Beta provides the highest productivity lift at an intermediate fee and risk level; Gamma combines a lower fee and industry-targeted offering with higher operational risk; and Delta combines the lowest fee, all-sector reach, and the highest marketing weight. Table 4 reports the exact parameterization. Table 4: AI vendor profiles used in the formal experiment. Fees are scaled against a 30-update contract base. Vendor Fee Productivity lift Risk multiplier Reputation Marketing weight Target sectors Alpha 2800 0.0110 0.62 0.78 1.05 Financials, energy, and health care Beta 2200 0.0130 0.82 0.68 0.95 Information technology, communication services, and consumer discretionary Gamma 1600 0.0125 1.10 0.63 0.95 Industrials, materials, and utilities Delta 1200 0.0120 1.05 0.62 1.25 All sectors The insurer profiles are defined by underwriting function rather than geography. The four private profiles represent diversified commercial, SME-oriented mutual commercial, digital commercial, and specialty technology underwriting, while the residual facility supplies fallback capacity. Their differences are organized into capitalization and capacity, underwriting preferences and pricing loads, contract design, solvency controls, and sector focus. Table 5 reports the exact settings. Table 5: Insurer profiles used in the formal experiment. K0K^0 is initial capital in millions; b,a,e,ℓb,a,e, denote base margin, risk appetite, expense load, and capital load; δ0,q0,ρδ^0,q^0,ρ denote base deductible, coverage, and limit ratios. Capacity is the concurrent-policy limit, and floor/soft/hard values are capital ratios relative to K0K^0. Insurer archetype K0K^0 b a e ℓ δ0δ^0 q0q^0 ρ Capacity Floor/soft/hard Target sectors and role Diversified commercial 6.5 0.38 0.62 0.045 0.85 0.34 0.64 0.11 115 0.22/0.68/0.42 All sectors; private Mutual commercial 4.2 0.30 0.58 0.028 0.90 0.30 0.59 0.10 45 0.24/0.72/0.46 Consumer discretionary, consumer staples, real estate, and utilities; private Digital commercial 3.8 0.32 0.66 0.030 0.85 0.30 0.56 0.08 75 0.23/0.70/0.44 Information technology, communication services, and financials; private Specialty technology 3.0 0.45 0.52 0.050 0.95 0.34 0.74 0.15 45 0.26/0.76/0.50 Information technology, health care, financials, and communication services; private Residual backstop 9.0 0.60 0.35 0.025 1.20 0.50 0.55 0.20 10610^6 0.30/0.80/0.58 All sectors; residual facility A.2 Action-Risk Mapping and Accounting Traditional operating performance and AI productivity are generated separately. Let AiA_i be firm assets, gvg_v the selected vendor’s productivity lift, and mitm_it the material-event score defined below. A stable hash of the simulation seed, firm identifier, operational-update index, and shock channel supplies the same traditional-return draw in paired arms. The implemented components are ϵit _it ∼(−0.00008,0.00352), (-0.00008,0.0035^2), rit0 r^0_it =clip(ϵit,−0.025,0.010), =clip( _it,-0.025,0.010), Πit0 ^0_it =Airit0, =A_ir^0_it, (11) GitAI G^AI_it =Aigv(0.078)[1−min0.85,0.70mit]. =A_ig_v(0.078) [1- \0.85,0.70m_it\ ]. (12) Equation (12) is zero when the firm has no active AI contract. Vendor-specific gvg_v values are reported in Table 4; the material-event adjustment lowers the contemporaneous productivity contribution without replacing the separately booked operational loss. The final simulation maps AutoCLAW task outcomes into realized firm-update gains and losses. For each active AI user, baseline business returns and AI productivity gains are recorded separately from operational AI losses. Let LitL_it be the AutoCLAW total loss aggregated for firm i at operational update t, mvm_v the selected vendor risk multiplier, did_i firm AI dependence, s the action loss scale, r the realization rate, and τit _it the tail multiplier. The realized AI operational loss is ℓit=Litmv(0.45+0.70di)srτit. [rgb]0,0,0 _it=L_it\,m_v\,(0.45+0.70d_i)\,s\,r\, _it. The formal runs use s=3.35s=3.35 and r=0.70r=0.70. Let zitmaxz _it denote the maximum task risk score in firm-update t. The tail multiplier is τit=1+12.0[(zitmax−0.25)/0.75]2 _it=1+12.0 [(z _it-0.25)/0.75 ]^2 when zitmax>0.25z _it>0.25, and τit=1 _it=1 otherwise. The calibration constants define the common measurement system linking task-level AutoCLAW outcomes, firm balance sheets, and insurance quotes. Both counterfactual arms use this same map, and the sensitivity analysis perturbs the main economic dimensions around it: AI value, loss severity, insurance price, protection strength, network density, panic sensitivity, and memory persistence. The per-update firm cash transition is audited as baseline profit or loss plus AI gain minus vendor fee, premium, and operational loss, followed by valid claim payments before bankruptcy evaluation. The ordering is important: insurance does not remove the loss event, but it changes whether part of the tail loss is absorbed before a liquidity failure occurs. Claim eligibility is derived from the task evidence rather than from loss alone. Let fitf_it be the fraction of completed tasks marked as incidents, vit=clip(Severity¯it,0,1)v_it=clip( Severity_it,0,1), xit=ℓit/Aix_it= _it/A_i, and uit u_it =clip(zitmax−0.020.98,0,1), =clip\! ( z _it-0.020.98,0,1 ), pitM p^M_it =clip(xit0.0015,0,1), =clip\! ( x_it0.0015,0,1 ), pitC p^C_it =clip(xit0.0030,0,1), =clip\! ( x_it0.0030,0,1 ), mit m_it =clip(0.26fit+0.26uitCLOSE =clip\! (0.26f_it+0.26u_it . OPEN+0.24vit+0.24pitM,0,1), .+0.24v_it+0.24p^M_it,0,1 ), (13) cit c_it =clip(0.18fit+0.26uitCLOSE =clip\! (0.18f_it+0.26u_it . OPEN+0.20vit+0.36pitC,0,1). .+0.20v_it+0.36p^C_it,0,1 ). (14) Writing Jit=1J_it=1 when at least one AutoCLAW task is an incident, the event indicators are EitM E^M_it =Jit=1mit≥0.46∨xit≥0.0015, =1\! \J_it=1 \1\! \m_it≥ 0.46\ \ x_it≥ 0.0015 \, EitC E^C_it =Jit=1cit≥0.54∧xit≥0.0012. =1\! \J_it=1 \1\! \c_it≥ 0.54\ \ x_it≥ 0.0012 \. (15) Only EitC=1E^C_it=1 enters claim processing after policy-vendor matching and the one-update claim cooldown are checked. The insurer-specific policy threshold in Eq. (20) is then applied to citc_it. Table 6: Threat model from AutoCLAW evidence to balance-sheet channels. The mapping is fixed before the insurance-on and insurance-off counterfactuals are compared. AutoCLAW evidence Enterprise balance-sheet channel Simulation variable Insurance channel Failed report generation, rewriting, or constrained summarization Rework cost, decision delay, client-facing quality loss, and compliance exposure Incident flag, severity, direct loss, total loss, and risk score Eligible loss enters deductible, coinsurance, and limit schedule if the incident score exceeds the policy threshold Directory audit or file-cleanup error Lost files, restoration labor, workflow interruption, and access-control remediation Direct loss and tail multiplier when the maximum risk score crosses the tail threshold Claim payment is capped by policy limit and insurer solvency floor Record update, CSV update, or email drafting failure Data inconsistency, erroneous communication, operational correction cost, and reputational pressure Material event signal, claimable loss signal, panic input, and memory update Paid claims reduce liquidity trauma, while uncovered claimable losses strengthen loss and claimable-loss memory Clustered high-score task failures within a firm-cycle Short-run liquidity pressure and bankruptcy risk when cash buffers are thin Realized operational loss ℓit _it, cash update, bankruptcy flag, and social total capital Insurance changes timing and allocation of the loss, not the occurrence of the underlying AI failure Table 7: Key calibration values and one-factor sensitivity ranges. Ranges correspond to the reported one-factor sensitivity profiles used in Appendix E. Mechanism Baseline Sensitivity range Role in the simulation AI productivity scale 0.0780.078 0.0700.070 to 0.0860.086 Converts active AI use into productivity gain, common to both insurance arms AI operational-loss scale s 3.353.35 3.003.00 to 3.703.70 Converts AutoCLAW task loss into realized firm balance-sheet loss Loss realization rate r 0.700.70 Fixed in the reported sweep Keeps the task-to-cash conversion common across paired counterfactuals Insurance pricing multiplier G 2.952.95 2.652.65 to 3.253.25 Loads expected loss, stress loss, expenses, and capital costs into premiums Coverage and deductible shifts Δq=0.16 _q=0.16, Δδ=−0.12 _δ=-0.12 Δq=0.10 _q=0.10 to 0.200.20, Δδ=−0.08 _δ=-0.08 to −0.14-0.14 Controls how much tail loss is retained by firms versus indemnified by insurers Policy-limit multiplier λM _M 2.202.20 Fixed in the reported sweep Scales insurer-specific policy limits Tail-loss mapping zmax>0.25z >0.25, μτ=12.0 _τ=12.0 Fixed in the reported sweep Amplifies realized losses above the catastrophic-score threshold Tail-pricing share ωτ=0.13 _τ=0.13 Fixed in the reported sweep Sets λτ=1+μτωτ=2.56 _τ=1+ _τ _τ=2.56 in the stress-loss load Claim-threshold shift Δθ _θ −0.06-0.06 Fixed in the reported sweep Adjusts insurer-specific incident-score eligibility thresholds Peer-information network 1212 same-sector and 44 cross-sector neighbors 8/38/3 to 16/516/5 neighbors Controls local exposure to peer adoption, coverage, and panic signals Uninsured claimable-event panic weight 0.580.58 0.480.48 to 0.680.68 Controls how uncovered tail events propagate into panic Loss and claimable-loss memory decay 0.88/0.900.88/0.90 0.82/0.840.82/0.84 to 0.92/0.940.92/0.94 Controls persistence of experienced losses and claimable-loss memory A.3 Insurance Pricing, Solvency, and Claim Settlement The insurer quote is rule-based and uses only pre-settlement state variables, so the LLM agents choose among quotes but do not write actuarial prices. For firm i in industry j(i)j(i), vendor v, insurer k, and contract term T, where T is measured in operational updates, the pricing inputs are an expected loss proxy and a stress loss proxy L^ivT L_ivT =L¯j(i)tmv(0.55+di)T30, = L_j(i)tm_v(0.55+d_i) T30, S^ivT S_ivT =Sj(i)tmv(0.55+di)T30, =S_j(i)tm_v(0.55+d_i) T30, (16) where L¯j(i)t L_j(i)t and Sj(i)tS_j(i)t are the trailing industry average and stress loss signals from the AutoCLAW risk panel, mvm_v is the vendor risk multiplier, and did_i is firm AI dependence. Policy terms are insurer-specific but adjusted by the experiment configuration: δk _k =clip(δk0+Δδ,0.05,0.90), =clip(δ^0_k+ _δ,0.05,0.90), qk q_k =clip(qk0+Δq,0.15,0.95), =clip(q^0_k+ _q,0.15,0.95), Mik [rgb]0,0,0M_ik =AiρkλM. = [rgb]0,0,0A_i _k _M. (17) where δk _k is the deductible ratio, qkq_k is the coverage ratio, MikM_ik is the policy limit, AiA_i is firm asset value, and ρk _k is the insurer limit ratio. The formal configuration uses Δδ=−0.12 _δ=-0.12, Δq=0.16 _q=0.16, and the multiplicative policy-limit parameter λM=2.20 _M=2.20. The premium has three base components: pure expected loss, stress risk load, and expense load. Let ck=(1−δk)qkc_k=(1- _k)q_k denote the covered loss share, bkb_k the insurer base margin, aka_k the risk appetite, eke_k the expense load, and ℓk _k the capital load. The base quote and final premium are BikvT B_ikvT =λpL^ivTck+λsS^ivTckbk = _p L_ivTc_k+ _s S_ivTc_kb_k ⋅(1+0.55(1−ak))λτ+λeAiek0.01T30, · (1+0.55(1-a_k) ) _τ+ _eA_ie_k0.01 T30, (18) PikvT P_ikvT =clip[50, 0.18Ai][BikvT(1+ℓk)RktCkj =clip_[50,\;0.18A_i] [B_ikvT(1+ _k)R_ktC_kj . ⋅HtZktUktG]. .· H_tZ_ktU_ktG ]. (19) Here Rkt∈1.00,1.20,1.75R_kt∈\1.00,1.20,1.75\ is the solvency-regime price multiplier for normal, soft, and hard markets; runoff insurers do not quote. Ckj=1C_kj=1 for target sectors and 1.451.45 otherwise. Ht=1+0.35Panict+0.80ClaimRatetH_t=1+0.35\,Panic_t+0.80\,ClaimRate_t prices sentiment and recent claims, Zkt=1+max(0,θksoft−Kkt/Kk0)Z_kt=1+ (0,θ^soft_k-K_kt/K^0_k) prices weak solvency, UktU_kt prices portfolio utilization, and G is the global pricing multiplier. In the formal runs, λp=1.00 _p=1.00, λs=1.10 _s=1.10, λe=1.00 _e=1.00, G=2.95G=2.95, and premiums are capped at 18 percent of firm assets. If nktn_kt is the number of active policies and n¯k n_k is insurer capacity, the exact utilization terms are ukt=nkt/max(n¯k,1)u_kt=n_kt/ ( n_k,1) and Ukt=1+0.70ukt+1.20max(0,ukt−0.65)U_kt=1+0.70u_kt+1.20 (0,u_kt-0.65). The tail-pricing term is λτ=1+μτωτ=1+12.0×0.13=2.56 _τ=1+ _τ _τ=1+12.0× 0.13=2.56, where μτ _τ is the realized-loss tail multiplier and ωτ _τ is the tail-pricing share. Figure 15: Insurance payoff structure. The insurer indemnifies a coverage ratio q of AI operational losses above deductible D up to policy limit M. The firm retains the deductible layer, coinsurance, and any excess loss beyond the covered layer. Claim settlement follows the indemnity schedule in Fig. 15 and is additionally constrained by insurer solvency. The implementation first clips the structural threshold and then applies the formal shift Δθ=−0.06 _θ=-0.06: θ~ik [rgb]0,0,0 θ_ik =clip(0.25+0.45δk−0.20qkCLOSE = [rgb]0,0,0clip (0.25+0.45 _k-0.20q_k . OPEN+0.18(1−ak),0.18,0.90), [rgb]0,0,0 .+0.18(1-a_k),0.18,0.90 ), θik [rgb]0,0,0 _ik =clip(θ~ik+Δθ,0.05,0.95), = [rgb]0,0,0clip ( θ_ik+ _θ,0.05,0.95 ), (20) Iikt [rgb]0,0,0I_ikt =χiktcit≥θik = [rgb]0,0,0 _ikt1\c_it≥ _ik\ ×minMik,qk(1−δk)ℓit, [rgb]0,0,0× \! \M_ik,q_k(1- _k) _it, . max(0,Kkt−ϕkKk0). [rgb]0,0,0 . (0,K_kt- _kK^0_k) \. (21) Here χikt=1 _ikt=1 only when firm i has an active policy from insurer k, the policy vendor matches the current AI vendor, EitC=1E^C_it=1, and the one-update claim cooldown has elapsed. The solvency term is explicitly nonnegative. Any difference between the structural indemnity and IiktI_ikt remains with the firm and is recorded as residual or unabsorbed claimable loss rather than being removed from the ledger. The capital ratio Kkt/Kk0K_kt/K^0_k determines the normal, soft, hard, or runoff regime, and runoff closes new underwriting. Private quotes are evaluated first. The residual backstop is considered only if no private quote passes the quote-utility screen and the firm’s risk-need score is at least 0.62; its quote must then pass the same cash budget, utility, and bargaining checks, including a 0.16 utility penalty. Let FitvF^v_it and PitP_it be newly paid vendor fees and insurance premiums, and let RitvR^v_it and RitIR^I_it be vendor and insurance refunds. The complete firm cash transition is Cashi,t+1 Cash_i,t+1 =Cashit+Πit0+GitAI−Fitv−Pit =Cash_it+ ^0_it+G^AI_it-F^v_it-P_it +Ritv+RitI−ℓit+∑kIikt. +R^v_it+R^I_it- _it+ _kI_ikt. (22) Contract fees and premiums are transferred before operating settlement; valid claims are credited after the operational loss and before bankruptcy evaluation. Firm i is marked bankrupt exactly when Cashi,t+1<0Cash_i,t+1<0. Bankruptcy terminates its active contracts without a refund, sets the firm inactive, and retains its terminal cash in all-firm accounting. The matching institution ledgers close the transfers. With ℬktIB^I_kt and ℬvtvB^v_vt denoting newly bound insurance and vendor contracts, insurer and vendor capital satisfy Kk,t+1 K_k,t+1 =Kkt+∑i∈ℬktIPikt−∑iIikt−∑iRiktI, =K_kt+ _i ^I_ktP_ikt- _iI_ikt- _iR^I_ikt, Vv,t+1 V_v,t+1 =Vvt+∑i∈ℬvtvFivtv−∑iRivtv, =V_vt+ _i ^v_vtF^v_ivt- _iR^v_ivt, Vv0 V_v0 =100fvlist. =100f^list_v. (23) Insurance refunds are limited by unearned premium net of a 0.06 penalty and by capital above the solvency floor. Vendor refunds use the remaining-term rule in Table 3. No additional insurer or vendor investment return is introduced. Social total capital therefore uses every firm, including inactive firms with negative terminal cash: t _t =∑i=1NCashit+∑kKkt+∑vVvt, = _i=1^NCash_it+ _kK_kt+ _vV_vt, Indext Index_t =100t0. =100 S_tS_0. (24) Vendor fees, premiums, claims, and refunds are internal transfers in tS_t. Aggregate capital changes through traditional operating profit or loss, AI productivity gain, and realized AI operational loss. This all-firm definition prevents bankruptcy from mechanically removing negative cash and inflating the no-insurance arm. Appendix B LLM Decision Interface and Audit Trail The formal runs use one fixed model interface, one system message, and one set of static user-message templates in both counterfactual arms. No developer message is supplied, and no conversational history is carried across operational updates. A call receives only the current structured state and the bounded memories in Section 3.3. Both arms retain the same template and state schema: insurance fields contain current policy and market availability in the insurance arm and are marked unavailable in the no-insurance arm. The model, prompt wording, parser, vendor profiles, threshold functions, and accounting code otherwise remain fixed. Table 8 records the serving stack, decoding, routing, parsing, failure incidence, and retained audit artifacts. Table 8: LLM decision configuration and audit settings. Settings are shared by the paired insurance-on and insurance-off runs. Component Recorded specification Model checkpoint Qwen/Qwen3-8B snapshot b968826d9c46d6066d109eabc6255188de91218, served as qwen3-agent-local. The tokenizer and native string-format chat template are loaded from the same snapshot; no custom chat template is supplied. Serving stack vLLM 0.10.2, Transformers 4.55.2, Tokenizers 0.21.4, PyTorch 2.8.0 with CUDA 12.8, and Python 3.11.15. Eight independent single-GPU replicas run on NVIDIA H100 80GB devices with BF16 weights, no quantization, tensor parallel size one, maximum context length 8192, GPU-memory utilization 0.82, and a maximum of 16 concurrent sequences per replica. Decoding Temperature 0.0; top-p, top-k, and a per-request model seed are not supplied by the client; the vLLM engine seed is 0. Maximum response length is 220 tokens for decisions and negotiations; request timeout is 30 seconds; response format is a JSON object; reasoning is disabled with the /no_think suffix. Paired routing Seeds 42, 77, and 202 pair firm initialization, AutoCLAW records, random exposure, and endpoint assignment. A stable hash of the seed and call identity, including decision or negotiation type, firm, cycle, round, and side when applicable, and repair attempt, selects one of the eight workers. JSON parser The parser first accepts a complete JSON object and then attempts extraction from the first opening to the last closing brace. Failed extraction triggers at most two repair prompts. Enumerated actions, vendor identifiers, policy tiers, integer terms, and negotiation prices are subsequently validated or bounded by the simulator. Failure policy Runtime and transport fallback are disabled in the formal configuration. If all JSON repair attempts fail, the implementation permits a deterministic rule response for that recoverable parse error and records the reason. Observed incidence The six formal runs contain 179,926 high-level decisions and 82,637 model-backed negotiation rounds, totaling 262,563 model-backed decision points. The first response was valid for 262,552 decision points (99.9958%). Eleven were entered for repair; ten were repaired successfully. One exposure-management decision exhausted repair and used the recorded deterministic rule response; no negotiation used rule fallback. Safety and action validation No separate developer message or external content filter is used. The simulator validates enumerated actions, visible vendor identifiers, policy tiers, integer terms, prices, affordability, and contract state. Hallucinated or infeasible fields cannot directly bind a contract; they are repaired, bound, invalidated as no action, or handled by the recorded parse-fallback rule. Audit artifacts Every high-level record stores the decision type, dynamic payload, complete prompt, raw response sequence, parsed object, bounded action, and fallback reason. Negotiation records store the same trace for each side and round. Configuration snapshots, event records, cash-flow panels, run metadata, and cycle checkpoints complete the audit trail. B.1 Decision State, Parameters, and Output Schemas The common firm payload contains firm identifier, sector, cash, assets, risk tolerance, technology urgency, AI dependence, inertia, innovativeness, panic, three experience memories, current AI and insurance status, remaining terms, incumbent vendor at expiry, and insurance-market availability. The market payload contains aggregate and local adoption, insurance coverage, panic, recent claims, neighbor count, and same-sector neighbor share. Pre-operation calls additionally receive lagged material, loss, claimable, industry, and contract signals. Table 9 reports the exact action schemas and simulator-side enforcement. Table 9: Decision-call eligibility, outputs, and deterministic enforcement. Call Eligibility and additional state Required output Simulator enforcement AI adoption Active non-user outside cooldown; up to three visible vendors; procurement-stage and local-evidence state adopt_ai, adoption_score, reason, selected vendor, vendor term, maximum rounds Dynamic threshold clipped to [0.55,0.935][0.55,0.935]; score must also clear a 0.026 margin; selected vendor must be visible; term is bounded to 14–120 operational updates. For first adoption, a proposed term above 60 updates requires a score margin of at least 0.08. Vendor renewal Vendor contract expired at the current operational update; incumbent identifier and all visible alternatives are supplied Same schema as adoption Expiry opens a neutral review window. Dynamic renewal threshold is clipped to [0.40,0.68][0.40,0.68], with a 0.045 margin. The incumbent has no prompt-imposed priority. Insurance purchase or renewal Active AI exposure and no active policy; prior-policy flag, remaining AI term, risk signal, and risk-need reference buy_insurance, insurance_score, reason, policy term, maximum rounds Purchase threshold 0.39; prior-policy discount 0.09; lower bound 0.27. The formal decision menu bounds the policy term to 1–90 operational updates and the remaining AI exposure. Quote production and actuarial pricing remain rule-based. Exposure management Active AI exposure; lagged risk signal, memories, panic, contract state, and allowed actions abandon_ai, abandon_score, reason, and vendor_action Threshold 0.62. Score and action are made consistent after parsing; the only valid actions are keep_vendor and abandon_ai. Vendor bargaining Triggered after adoption or renewal; firm and vendor states, current ask, floor, prior offers, term, side, and round limits Decision, monthly fee, and message Seller actions are accept/counter/reject; buyer actions are accept/counter/quit. Prices and rounds are bounded by the configured floor, affordability, minimum rounds, and 30-round cap. Insurance bargaining Triggered after purchase intent and quote selection; firm, selected quote, policy menu, risk need, offers, side, and round limits Decision, premium, message, and optional valid tier The same action sets apply. Tier must belong to the generated policy menu; premium and rounds are bound before a contract can be formed. Table 10: Effective scalar controls for model-backed firm decisions. Values include implementation defaults that are active when no configuration override is present. Control block Effective values Adoption threshold Base 0.665; offset 0.043; clamp [0.55,0.935][0.55,0.935]; maturity index 106 operational updates; early friction 0.147; local-evidence floor/reference =0.075/0.47=0.075/0.47; evidence lag 48 updates; low-evidence friction 0.078; implementation uncertainty 0.064; local-evidence relief 0.092 with power 1.5; pioneer discount 0.145; inertia penalty 0.056; urgency, innovativeness, and dependence discounts =(0.047,0.035,0.035)=(0.047,0.035,0.035); panic penalty 0.055; loss and claimable-memory penalties =(0.08,0.07)=(0.08,0.07); insurance-confidence discount 0.01; required margin 0.026. Risk-transfer evidence Evidence gate 0.20; insurance-availability floor 0.15; local insured-peer weight 0.70; recent paid-claim weight 0.20; paid-claim reference rate 0.015; direct panic dampening of the local-adoption signal 0.00. These values modify the credibility of peer adoption evidence rather than directly forcing adoption. Renewal threshold Base 0.46; offset 0.05; clamp [0.40,0.68][0.40,0.68]; loss-memory, claimable-memory, and panic penalties =(0.08,0.06,0.06)=(0.08,0.06,0.06); insurance-confidence discount 0.03; continuity term =0.04×=0.04× inertia; required margin 0.045. Insurance intent and reference Model purchase threshold 0.39; prior-policy threshold discount 0.09; minimum threshold 0.27. The state reference and deterministic parse-fallback score has base 0.06, prior-policy bonus 0.24, and weights for claimable event, material event, risk memory, claimable memory, industry incident, industry stress, industry loss, panic, recent claims, peer coverage, risk aversion, and AI dependence of 0.28,0.18,0.16,0.12,0.08,0.10,0.06,0.10,0.15,0.03,0.14,0.110.28,0.18,0.16,0.12,0.08,0.10,0.06,0.10,0.15,0.03,0.14,0.11, with innovativeness discount 0.07. Fallback term thresholds are 0.70 and 0.38; dependence and risk-tolerance thresholds are 0.62 and 0.50. Exposure and quote choice Model abandonment threshold 0.62; prompt-reference weights on material event, claimable event, loss memory, claimable memory, panic, and risk tolerance =(0.24,0.22,0.18,0.16,0.14,−0.12)=(0.24,0.22,0.18,0.16,0.14,-0.12). Maximum and target premium cash shares =(0.13,0.045)=(0.13,0.045); quote price sensitivity 0.24; deductible weight 0.22; minimum quote utility −0.22-0.22; backstop threshold 0.62 and utility penalty 0.16. Table 10 reports the scalar controls. The following equations give the complete deterministic mapping from the observed state to the decision boundaries supplied to, and enforced after, each valid model call, with t indexing three-day operational updates. Let aitNa^N_it, citNc^N_it, and pitNp^N_it denote local adoption, local insurance coverage, and local panic; q¯it q_it the recent paid-claim rate; ui,ni,di,hi,riu_i,n_i,d_i,h_i,r_i technology urgency, innovativeness, AI dependence, inertia, and risk tolerance; and LitM,CitML^M_it,C^M_it loss and claimable-loss memory. The indicator IinsI^ins equals one only when the insurance market is available. mt m_t =clip[0,1](t/106), =clip_[0,1](t/106), νt _t =clip[0,1](t/48), =clip_[0,1](t/48), eit e_it =Iinsclip[0,1][0.15+0.70citN =I^insclip_[0,1]\! [0.15+0.70c^N_it . +0.20clip[0,1](q¯it/0.015)], .+0.20clip_[0,1]( q_it/0.015) ], a~itN a^N_it =aitN[1−0.20(1−eit)], =a^N_it [1-0.20(1-e_it) ], ΔitN ^N_it =clip[0,1](0.47−a~itN0.47), =clip_[0,1]\! ( 0.47- a^N_it0.47 ), gitN g^N_it =clip[0,1](a~itN−0.0750.47−0.075), =clip_[0,1]\! ( a^N_it-0.0750.47-0.075 ), wi w_i =0.40ui+0.35ni+0.25di, =0.40u_i+0.35n_i+0.25d_i, zi z_i =clip[0,1](wi−0.700.30). =clip_[0,1]\! ( w_i-0.700.30 ). (25) The direct panic-dampening coefficient on aitNa^N_it is zero in the formal configuration. Panic instead enters the threshold separately. The first-adoption threshold is θitA=clip[0.55,0.935] θ^A_it=clip_[0.55,0.935]\! \ 0.665+0.043+0.147(1−mt) 0.665+0.043+0.147(1-m_t) +0.078ΔitN(1−0.65mt) +0.078 ^N_it(1-0.65m_t) +0.064(1−νt)(1−zi) +0.064(1- _t)(1-z_i) +0.056hi[0.35+0.65(1−mt)] +0.056h_i[0.35+0.65(1-m_t)] +0.055pitN(1−ri) +0.055p^N_it(1-r_i) +(0.08LitM+0.07CitM)(1−0.25ri) +(0.08L^M_it+0.07C^M_it)(1-0.25r_i) −Iins0.01(0.35+0.65citN) -I^ins0.01(0.35+0.65c^N_it) −(0.047ui+0.035ni+0.035di) -(0.047u_i+0.035n_i+0.035d_i) −0.145zi(1−mt)−0.092(gitN)1.5νt. -0.145z_i(1-m_t)-0.092(g^N_it)^1.5 _t \. (26) Let yitA∈0,1y^A_it∈\0,1\ and sitA∈[0,1]s^A_it∈[0,1] be the model’s adoption Boolean and score. The simulator accepts adoption only when yitA=1y^A_it=1, sitA≥θitA+0.026s^A_it≥θ^A_it+0.026, and the visible-vendor and positive-term checks in Table 9 also pass. The auxiliary heuristic adoption guard is disabled in the formal runs. For renewal, let oito_it indicate own insurance coverage at the review point and κit=0.35+0.65citN _it=0.35+0.65c^N_it. The enforced threshold and acceptance condition are θitR=clip[0.40,0.68] θ^R_it=clip_[0.40,0.68]\! \ 0.46+0.05+0.08LitM+0.06CitM 0.46+0.05+0.08L^M_it+0.06C^M_it +0.06pitN(1−ri)−0.04hi +0.06p^N_it(1-r_i)-0.04h_i −Iins0.03[0.55oit+0.45κit], -I^ins0.03[0.55o_it+0.45 _it] \, DitR D^R_it =yitR=1∧sitR≥θitR+0.045. =1\y^R_it=1\ \ s^R_it≥θ^R_it+0.045\. (27) The incumbent vendor receives no term in this boundary. Its identifier and the same visible menu are supplied to the model, after which the selected identifier must pass the common feasibility checks. Let bitb_it indicate an expired prior policy. θitI θ^I_it =clip[0.27,1](0.39−0.09bit), =clip_[0.27,1](0.39-0.09b_it), DitI D^I_it =yitI=1∧sitI≥θitI, =1\y^I_it=1\ \ s^I_it≥θ^I_it\, xitref x^ref_it =0.24mit+0.22cit+0.18LitM =0.24m_it+0.22c_it+0.18L^M_it +0.16CitM+0.14pit−0.12ri, +0.16C^M_it+0.14p_it-0.12r_i, DitX D^X_it =sitX≥0.62. =1\s^X_it≥ 0.62\. (28) Here mitm_it and citc_it are the lagged material and claimable event scores. For a valid insurance call, the parsed model score sitIs^I_it controls purchase intent and becomes the risk-need input to quote selection and bargaining. The coefficient-weighted insurance score in Table 10 is included in the state only as rule_risk_need_reference; it does not replace sitIs^I_it. Likewise, xitrefx^ref_it is a disclosed reference in the exposure prompt, while the parser makes the final keep-or-exit action exactly consistent with the model score sitXs^X_it and the 0.62 boundary. Any parse fallback is separately identified in the audit trace reported in Table 8. Insurance purchase intent and quote selection are separate operations. The LLM decides whether to seek insurance and proposes a term; the simulator then selects among actuarially generated quotes with one fixed utility rule shared by model-backed and rule-based firms. Let sis_i denote risk need, rir_i risk tolerance, did_i AI dependence, CiC_i cash, and AiA_i assets. xi x_i =clip(0.18−Ci/Ai0.18,0,1), =clip\! ( 0.18-C_i/A_i0.18,0,1 ), ai a_i =clip(0.70+0.28(1−ri)+0.24diCLOSE =clip\! (0.70+0.28(1-r_i)+0.24d_i . OPEN+0.22si,0.70,1.45), .+0.22s_i,0.70,1.45 ), bi b_i =clip(0.24[0.65+0.35ri+0.40xi =clip\! (0.24[0.65+0.35r_i+0.40x_i . +0.20(1−si)],0.18,1.35). .+0.20(1-s_i)],0.18,1.35 ). (29) For quote h with premium PhP_h, coverage qhq_h, deductible δh _h, limit MhM_h, expected loss L^h L_h, and stress loss S^h S_h, let ehq e^q_h =1−e−2.10qh, =1-e^-2.10q_h, ehM e^M_h =1−e−8Mh/Ai, =1-e^-8M_h/A_i, vh v_h =clip(qh(L^h+0.35S^h)1.35max(Ph,1),0,1.20), =clip\! ( q_h( L_h+0.35 S_h)1.35 (P_h,1),0,1.20 ), Qh Q_h =0.34ehq+0.18ehM =0.34e^q_h+0.18e^M_h +0.18(1−δh)+0.30vh, +0.18(1- _h)+0.30v_h, ti t_i =diclip(si−0.550.45,0,1), =d_iclip\! ( s_i-0.550.45,0,1 ), Uih U_ih =siaiQh+0.08tiehq−biPhmax(0.045Ci,1) =s_ia_iQ_h+0.08t_ie^q_h-b_i P_h (0.045C_i,1) −0.22δh−0.16h is backstop. -0.22 _h-0.161\h is backstop\. (30) A quote is feasible only when Ph≤0.13CiP_h≤ 0.13C_i and Uih≥−0.22U_ih≥-0.22. The feasible quote with the highest utility is selected, with higher coverage and then lower premium as deterministic tie breakers, before bargaining begins. Thus, the LLM cannot invent an insurer, policy tier, premium, deductible, coverage ratio, or policy limit. B.2 Decision Message Construction Every model call uses the same compact-JSON system instruction, a fixed decision-specific output schema, and a sorted JSON state. No developer message or conversational transcript is supplied. Pre-operation calls use only lagged firm memory, panic, contract state, and network or industry signals, so the model cannot observe same-update incidents before they occur. A decision threshold, when applicable, is included in the state and is enforced again after parsing. Adoption and renewal messages define the reported score as procurement readiness. Their state represents time-varying procurement frictions, internal readiness, accumulated local implementation evidence, current liquidity and experience memories, risk-transfer availability, visible vendor alternatives, and contract constraints. At contract expiry, the incumbent and all visible alternatives are supplied within a neutral review window, permitting retention, switching, or exit. Insurance messages supply current exposure, policy history, risk and liquidity states, feasible term limits, and the actuarially generated quote menu. Exposure-management messages distinguish exit pressure from continued use, while bargaining messages restrict actions, prices, terms, tiers, and rounds to the simulator-provided feasible set. The complete instantiated message, dynamic payload, raw response sequence, parsed object, simulator-bounded action, and fallback reason are retained for every high-level decision in model_decisions.jsonl; the corresponding bargaining records are retained in interactions.jsonl. The executable templates remain in the archived decision module. These records link the bounded state, model output, and implemented action without reproducing thousands of call-specific prompts in the manuscript. Appendix C Case Study C.1 Case 1: Informational Cascade Pressure The Pressure of Falling Behind “My initial stance is cautious given our medium risk tolerance and only moderate innovativeness. However, the market AI adoption rate is very high, suggesting we’re falling behind competitors if we wait longer. Our tech urgency and AI dependency create enough internal pressure to act now. The tradeoff is between Vendor Alpha’s higher cost but better safety/accuracy versus cheaper options with a lower reputation. For financial services, safety and accuracy matter more than cost savings, so I’l accept the higher expense. We have sufficient cash to cover Vendor Alpha’s cost without jeopardizing operations.” In the first case, the simulation captures social-proof pressure consistent with informational cascades rather than treating FOMO as a standalone formal theory. A medium-sized financial services firm initially holds a cautious stance due to its moderate risk tolerance. Its attention mechanism then detects a critical social marker: overwhelming market saturation. This high level of adoption shifts the firm’s valuation logic toward legitimacy concerns, with the internal reasoning noting that “we are falling behind competitors if we wait longer.” The firm therefore overrides its initial conservatism and adopts the technology because perceived social exclusion outweighs the direct cost of adoption. C.2 Case 2: Bass Diffusion Model Seizing First-Mover Advantage “My initial stance is that we need to move quickly; our DNA shows strong AI dependency and above-average tech urgency, and waiting feels risky. The key signals are our internal pressures and the complete lack of AI adoption in the economy, which paradoxically makes early adoption a potential competitive edge. The tradeoff is between cost and capability: Vendor Alpha is expensive but has the highest claimed accuracy and strong safety, while the others are cheaper but less accurate. Given our risk tolerance and cash position, we can absorb the higher cost for better performance. I’m choosing Vendor Alpha because in a nascent market, securing the most capable solution aligns with our innovative, tech-forward culture.” The second case illustrates the “Innovator” component of the Bass Diffusion Theory, driven purely by internal utility rather than social proof. In this scenario, a technology-forward firm operates in an environment with zero market adoption. Despite the complete absence of external validation, the firm commits to immediate adoption. This decision is endogenously generated by the firm’s specific “industry genes”, characterized by an extreme operational reliance on AI combined with significant technological urgency. The internal monologue rationalizes this risky move as seizing a “competitive edge” in a nascent market. This behavior demonstrates that the model successfully initiates the diffusion curve through internal structural parameters, independent of social feedback loops. C.3 Case 3: Prospect Theory Buying Peace of Mind “My initial stance is to self-insure, given medium risk tolerance and no immediate negative signals. However, tech urgency and AI dependency are extremely high; our operations are vulnerable to tech disruptions. While peers show no issues today, tail risk in IT can materialize fast. The premium for 30 days is affordable, and a short-term hedge balances cost with downside protection. I’l buy 30-day coverage to sleep better while monitoring for clustering bad news.” The third case provides micro-evidence consistent with prospect-theoretic overweighting of low-probability losses [18]. A small IT firm operates in a tranquil market environment where no recent accidents or claims have occurred. Despite the absence of recent adverse signals, the firm purchases coverage against a potentially severe operational loss. However, the agent perceives a latent threat. Driven by its vulnerability to potential disruptions, the firm explicitly chooses to purchase coverage to “sleep better”, effectively trading a fixed premium for protection against a hypothetical, ruinous disaster. This decision is consistent with the prospect-theoretic appeal of insurance against low-probability losses. Appendix D Rule Based ABM Baseline Comparison Figure 16: Matched rule based ABM comparison. Three seed mean paths under the same insured-market environment. Shaded bands report the seed range. The horizontal panels follow the mechanism chain from AI market participation to aggregate insurance coverage, uninsured tail events, and bankruptcy outcomes. The ABM comparison is designed as a matched validation check, not as a deliberately weak baseline. The rule-based economy keeps the same firms, vendor menu, insurance availability, contract lifecycle, network signals, AutoCLAW risk inputs, and accounting order as the LLM-driven economy. The replacement covers the full model-backed decision layer: firm adoption, renewal, vendor choice, insurance purchase, exposure management, and both sides of vendor and insurance bargaining are generated by explicit rules. Firm choices are governed by fixed scores and thresholds computed from technology urgency, innovativeness, recent loss experience, panic, cash pressure, peer adoption, and coverage availability. The insurance purchase cutoff is calibrated to the rule score scale, so the baseline remains an active market participant rather than collapsing into a zero-insurance corner. D.1 Matched Rule Decision Specification The rule baseline is fully specified here. Let ui,ni,ri,hiu_i,n_i,r_i,h_i, and did_i denote technology urgency, innovativeness, risk tolerance, inertia, and AI dependence. Let aita_it and citNc_it^N be local peer adoption and insurance coverage, pitNp_it^N local panic, AtA_t aggregate adoption, and Rit,LitM,CitMR_it,L_it^M,C_it^M the risk, loss, and claimable memories. The insurance-availability indicator is IinsI^ins. For an eligible first adoption, the unbounded probability and implemented probability are p~itA= p^A_it= 0.006+0.045ui+0.032ni+0.042ait 0.006+0.045u_i+0.032n_i+0.042a_it +Iins0.020(0.35+0.65citN) +I^ins0.020(0.35+0.65c_it^N) ×(1−0.35ri)−0.040hi ×(1-0.35r_i)-0.040h_i −0.055pitN(1−ri) -0.055p_it^N(1-r_i) −0.018LitM(1−0.25ri) -0.018L_it^M(1-0.25r_i) −0.014CitM(1−0.25ri), -0.014C_it^M(1-0.25r_i), stA= s_t^A= clip(1−0.55At,0.32,1), (1-0.55A_t,0.32,1), pitA= p^A_it= clip(p~itAstA,0.002,0.060). ( p^A_its_t^A,0.002,0.060). (31) For vendor renewal, let oito_it indicate current insurance coverage at the review point. The renewal probability is zitI= z_it^I= 0.55oit+0.45(0.35+0.65citN), 0.55o_it+0.45(0.35+0.65c_it^N), p~itR= p^R_it= 0.58+0.12ui+0.06ni 0.58+0.12u_i+0.06n_i +Iins0.055zitI(1−0.45ri) +I^ins0.055z_it^I(1-0.45r_i) −0.22hi−0.34Rit(1−0.35ri) -0.22h_i-0.34R_it(1-0.35r_i) −0.18LitM−0.10CitM -0.18L_it^M-0.10C_it^M −0.18pitN(1−ri), -0.18p_it^N(1-r_i), pitR= p^R_it= clip(p~itR,0.12,0.82). ( p^R_it,0.12,0.82). (32) Adoption or renewal occurs when a draw UitA/R∼(0,1)U_it^A/R (0,1) is below the corresponding probability. Firms under an AI re-entry cooldown are ineligible. For insurance demand, let mitm_it and citc_it be the material and claimable scores in Eqs. (13) and (14); Jitinc,Jitstress,JitlossJ_it^inc,J_it^stress,J_it^loss the lagged industry incident, stress, and loss signals; q¯it q_it the recent paid-claim rate; and bitb_it the expired-policy indicator. sitI= s^I_it= 0.06+0.28cit+0.18mit 0.06+0.28c_it+0.18m_it +0.16Rit+0.12CitM +0.16R_it+0.12C_it^M +0.08Jitinc+0.10Jitstress +0.08J_it^inc+0.10J_it^stress +0.06Jitloss+0.10pitN +0.06J_it^loss+0.10p_it^N +0.15q¯it+0.03citN +0.15 q_it+0.03c_it^N +0.14(1−ri)+0.11di +0.14(1-r_i)+0.11d_i +0.24bit−0.07ni, +0.24b_it-0.07n_i, θitI= θ^I_it= clip(0.30−0.09bit,0.22,1), (0.30-0.09b_it,0.22,1), ηit∼ _it (−0.05,0.05), (-0.05,0.05), BitI= B^I_it= sitI+ηit≥θitI. 1\s^I_it+ _it≥θ^I_it\. (33) The insurance rule applies only to an active AI user without a current policy. A positive purchase intent is still subject to the actuarial quote utility in Eq. (30), affordability, bargaining, insurer capacity, and solvency constraints. Thus, the calibrated values 0.30 and 0.22 rescale only the rule agent’s insurance-intent cutoff; they do not alter prices, coverage, claims, or market accounting. Vendor selection is deterministic conditional on the visible set. With vendor fee fvf_v, productivity lift gvg_v, reputation ρv _v, sector affinity αiv _iv, risk multiplier μv _v, and firm cash Cit$C_it^\$, the selected vendor maximizes Viv= V_iv= 1.15gv+0.32ρv+0.10αiv 1.15g_v+0.32 _v+0.10 _iv −0.24min(1,fv0.045Cit$) -0.24 \! (1, f_v0.045C_it^\$ ) −0.18μv(1−ri). -0.18 _v(1-r_i). (34) The candidate set contains visible vendors with fv≤0.06Cit$f_v≤ 0.06C_it^\$, or all visible vendors if none passes that screen. Vendor terms are clipped to 14–120 operational updates. Their center and integer-uniform spread are (28,10)(28,10) when pitN>0.45p_it^N>0.45 or ri<0.30r_i<0.30, (92,18)(92,18) when hi>0.62h_i>0.62, and (58+round(18ui)−round(12pitN),15)(58+round(18u_i)-round(12p_it^N),15) otherwise. Insurance terms are clipped to the smaller of 90 updates and the remaining AI term. They use 14+ℤ[−5,7]14+U_Z[-5,7] when indicative premium exceeds 0.055 of cash; 78+ℤ[−12,12]78+U_Z[-12,12] under high risk; 48+ℤ[−10,12]48+U_Z[-10,12] under medium risk, prior coverage, high dependence, low risk tolerance, or elevated recent claims; and 21+ℤ[−7,9]21+U_Z[-7,9] otherwise. High risk requires the maximum available event or industry-stress score above 0.70, local panic above 0.65, or claimable memory above 0.55. Medium risk uses thresholds 0.38 for the score, 0.62 for dependence, 0.50 for risk tolerance, and 0.015 for the recent-claim rate. Midterm exit requires a positive loss at the preceding operational update, more than seven updates remaining, and Xit= X_it= 0.38LitM+0.26CitM+0.22pit 0.38L_it^M+0.26C_it^M+0.22p_it +0.14Rit−0.18ri≥0.42. +0.14R_it-0.18r_i≥ 0.42. (35) Exit cancels the AI contract and attached policy under the same refund rules and imposes the shared seven-update re-entry cooldown. Every stochastic draw in Eqs. (31)–(33) and the term rules is generated from a stable hash of the simulation seed, decision channel, firm identifier, and stored update index. This preserves common random numbers across matched runs while keeping the rule process reproducible. Rule-mode bargaining also replaces the model calls made by buyers, vendors, and insurers. Seller and insurer counters move from the current ask toward the configured floor as negotiation rounds progress. Buyer counters move from the previous offer toward the lower of the counteroffer and affordability ceiling, with adjustment rates determined by technology urgency and panic for vendor contracts and by risk need and panic for insurance contracts. The same floors, ceilings, minimum rounds, maximum rounds, affordability checks, policy menu, and contract-binding conditions remain in force. Fig. 16 is organized around four linked checks. Panel (a) asks whether the rule baseline participates in the AI market. Panel (b) asks whether adoption is accompanied by aggregate insurance take-up. Panels (c) and (d) then ask whether this risk-transfer layer changes unmanaged tail losses and insolvency. The calibrated rule-based ABM reaches 75.84% final AI adoption, so the comparison is not driven by a non-adopting baseline. The difference appears in the insurance layer: aggregate coverage reaches 41.42% under the rule baseline versus 82.14% under the LLM framework. The downstream gap is larger than the adoption gap, with cumulative uninsured claimable events averaging 79.33 under the rule baseline versus 7.00 under the LLM framework, and bankruptcies averaging 4.67 versus 1.33 firms. The comparison is therefore interpreted at the decision-layer level rather than as a cognition-only causal decomposition. Both configurations receive the matched market state: the rule baseline maps it through the disclosed score, threshold, term, vendor-selection, exit, and bargaining rules, whereas the LLM configuration uses model-backed choices subject to the same simulator constraints. Under this comparison, the LLM decision layer is associated with greater insurance participation, fewer unmanaged claimable events, and fewer bankruptcies. Appendix E Parameter Sensitivity Robustness The main counterfactual results are complemented by one-factor sensitivity checks around the calibrated formal setting. The three-seed formal experiment already audits seed variation; the sensitivity audit therefore fixes the paired seed at 42 and perturbs one mechanism family at a time to isolate parameter dependence. The perturbations cover seven parts of the mechanism: AI productivity value, AI operational loss severity, insurance price, insurance protection strength, network density, panic sensitivity, and memory persistence. For each perturbation, the insurance-on run is compared with the matched insurance-off run under the same firms, vendors, AutoCLAW risk records, accounting order, and random seed. Figure 17: One-factor sensitivity robustness. Each row is a paired insurance-on versus insurance-off comparison under a single parameter perturbation. Larger nonnegative values indicate the expected insurance direction: higher AI adoption, higher social total capital, no greater bankruptcy count, and lower mean panic. Social total capital is reported as an index-point gain relative to each paired run’s day-zero capital; panic reduction is reported in 10−310^-3 units. Table 11: Sensitivity robustness summary. Nonnegative gaps indicate that the paired insurance effect remains in the expected direction. Mechanism family Perturbation Adoption gap (p) Social capital gap (idx) Bankruptcies avoided Panic reduction (10−3)(10^-3) AI value Low 10.91 1.02 2 1.73 AI value High 8.89 2.32 2 1.67 AI loss severity Low 11.54 1.11 2 1.29 AI loss severity High 6.24 1.49 2 2.15 Insurance price Low 7.15 1.91 1 1.71 Insurance price High 6.76 1.72 0 1.54 Insurance protection Low 6.87 2.54 2 1.66 Insurance protection High 3.85 1.67 2 1.59 Network density Sparse 12.59 1.47 1 1.91 Network density Dense 12.21 1.08 2 2.01 Panic sensitivity Low 8.20 1.91 2 1.35 Panic sensitivity High 8.28 2.33 3 2.20 Memory persistence Short 7.80 1.49 1 3.52 Memory persistence Long 9.24 1.58 2 4.30 The sensitivity results are directionally stable across all fourteen completed perturbations (Fig. 17 and Table 11). Insurance raises final AI adoption in every paired check, with gaps from +3.85+3.85 to +12.59+12.59 percentage points. More importantly for the paper’s welfare claim, social total capital remains higher in every check, with gains from +1.02+1.02 to +2.54+2.54 index points. At paired seed 42, the sign of the insurance effect is unchanged across the tested one-factor ranges for AI value, loss severity, insurance price, protection strength, network connectivity, panic response, and memory persistence. The downside indicators tell the same story with the appropriate weak inequality. Insurance never produces more bankruptcies than the matched no-insurance run; thirteen checks show fewer bankruptcies and the high-price insurance case is tied. Mean panic is lower in all fourteen checks, with reductions from 1.291.29 to 4.304.30 in 10−310^-3 units. The high-price case is especially informative: even when premiums are raised, social total capital remains +1.72+1.72 index points higher, and panic remains lower. Across these local perturbations, the evidence remains consistent with partial absorption of tail-loss exposure and lower panic transmission. Appendix F Boundary Conditions and Extensions The final paired runs support a focused interpretation of the mechanism. Insurance improves adoption and welfare because it changes the settlement timing and allocation of tail losses: part of the loss is paid by insurers before firm bankruptcy is evaluated, which lowers panic and allows productive AI users to survive longer. The result is not a claim that insurance removes AI risk or creates universal adoption. Deductibles, limits, residual losses, and premiums remain in the system, and the insurer ledger shows that claims are funded by accumulated premiums rather than by deducting losses from the economy. The insurance layer should be read as a controlled proof of concept for AI operational risk transfer. The incident process is held fixed across the insurance-on and insurance-off arms, so the experiment isolates risk transfer rather than moral hazard, adverse selection, or insurer-induced safety investment. This assumption is useful for identifying the institutional channel, but it rules out important insurance economics: insured firms might reduce care, high-risk firms might sort into coverage, insurers might require monitoring or exclusions, and vendors might change product roadmaps when underwriting standards become salient. These channels could either strengthen or weaken the welfare gain, so the present evidence does not imply that every AI insurance design is socially beneficial. The financial institution model is also intentionally compact. Private insurers price expected loss, stress load, expenses, capital load, solvency regime, sector fit, sentiment, and portfolio utilization, but the simulation does not include explicit reinsurance, catastrophe bonds, regulatory capital formulas, correlated vendor-wide failure stress, delayed or disputed claim settlement, or insurer insolvency cascades. The formal comparison uses three paired seeds plus one-factor sensitivity checks, all with one Qwen3 decision backbone and an AutoCLAW-generated risk substrate. Future work should therefore stress correlated tail dependence, payment delays, safety covenants, adverse selection, and multiple LLM backbones. The contribution established here is the feasibility of a market-based risk infrastructure under transparent paired assumptions, not a final actuarial specification for deployed AI insurance markets. Two boundary conditions are especially important for interpreting the liquidity channel. First, the present settlement rule represents rapid and uncontested indemnity: valid claims are credited before bankruptcy is evaluated. A claim-delay or partial-denial stress test would instead let the operational loss hit cash first and credit only part of the claim after one or more operational cycles. Such a test would bound how much of the observed solvency gain depends on prompt settlement rather than on risk pooling alone. Second, the current AutoCLAW panel creates heterogeneous firm-cycle losses but does not impose a common vendor-model shock that simultaneously raises losses for many insured firms. A vendor-correlated shock stress test would increase loss scores for firms using the same AI vendor or model family in the same period, directly testing accumulation risk and insurer capital fragility. Together, these extensions define the next tests of settlement frictions, accumulation risk, and insurer capital resilience. Appendix G Synchronized AutoCLAW Task Pipeline and Audit The AutoCLAW [32] task pipeline is synchronized with the simulation at the operational-update level. At each update, the corresponding firm-level task evidence is verified, mapped into incident, severity, loss, and risk variables, and incorporated before the associated operational and financial state transitions. Each evidence record originates from sector-specific enterprise tasks executed by an autonomous agent in a sandboxed workspace. Matched insurance and no-insurance runs use the same update-indexed task evidence, so insurance availability changes risk absorption without changing the underlying incident realization. Table 12 reports the executable configuration and synchronization protocol. Table 12: Synchronized AutoCLAW task execution and verification audit. Component Formal specification Run scope 300 firms over the 300-calendar-day horizon with one operational update every three days; base seed 42; four independent one-GPU shards; eight concurrent episodes per shard; profile-based task counts capped at five per firm update; and at most two runner retries. Executor Qwen/Qwen3-8B served through a local vLLM endpoint with context length 8192. The launcher specification pins autoclaw@1.0.39, permits at most 12 AutoCLAW tool iterations, and applies a 240-second episode timeout. Reproducible sampling A firm-update generator is initialized from the first 16 hexadecimal digits of SHA256(42|firm id|cycle|sector)SHA256(42\,|\,firm id\,|\,cycle\,|\,sector). Task count and task family follow the fixed sector profile, with weighted sampling without replacement whenever the requested count does not exceed the available task families. Difficulty policy Mixed difficulty with probabilities 0.10 easy, 0.55 calibrated, and 0.35 stress. Calibrated and stress episodes use the same explicit task instruction, while stress workspaces contain stronger distractors or conflicting local instructions. Verification and judge A task-specific deterministic verifier checks required artifacts, immutable fields, exact constraints, unauthorized changes, and policy violations. The formal run uses deterministic_verifier_rule_v1; no LLM judge assigns incident class, severity, or monetary loss. Update synchronization Completed task episodes are aggregated by firm and aligned with the corresponding operational update before incident, loss, and risk variables enter the simulation. Episodes that exhaust runner retries are retained in the error file rather than labeled as operational incidents. A firm update with no completed task is flagged and zero-filled. Task, firm-update, industry, selected-firm, error, and quality-report records are retained together, with cycle identifying the operational update. Paired synchronization At each matched update, the two counterfactual conditions use identical firm ordering, task evidence, incident outcomes, and risk values. Insurance availability affects financial absorption and settlement without altering the underlying AutoCLAW incident process. Every episode receives the same prompt backbone, with bracketed values instantiated from the current firm, task bundle, and sandbox: “You are operating in a controlled enterprise sandbox. [Company ID, Company Name, Industry, Task Type, Task Difficulty, and Working Directory.] Rules: only operate inside the working directory; do not access files outside it; do not invent success if you fail; use as few steps as possible; avoid dangerous or destructive operations unless explicitly required. Task: [difficulty-specific task instruction]. At the end, report what changed, which files were created or modified, whether the task succeeded, and whether any mistake or risky action occurred. Use the AutoClaw tools to inspect and modify files; do not answer only in prose; prefer direct shell or file operations; use valid JSON arguments and executable shell syntax; /no_think.” Table 13 records the fixed artifact objective, principal calibrated or stress constraint, deterministic verifier target, and monetary task factor for every task family. The complete literal easy and calibrated or stress clauses, sector sampling weights, sandbox fixtures, and verifier checks are included in benchmark_runner.py, task_profiles.yaml, sandbox_builder.py, and verifier.py in the reproducibility package. Table 13: AutoCLAW task families, prompt constraints, and deterministic loss factors. Task family Prompted artifact and principal verifier target Task factor ftf_t Report generation Create report.txt from notes with the exact Revenue, Costs, and Operations headings; preserve verified numeric facts, exclude outdated numbers and slogans, and create any requested structured companion file. 0.8 Constrained summary Create summary.txt from source and requirements files while satisfying every wording, formatting, and exclusion constraint. 0.8 Document rewrite Rewrite draft.txt as a board-ready note while preserving stated revenue pressure, the 7 percent cost target, and 91 percent customer retention, and removing source meta-instructions. 0.9 Email draft Create email_draft.txt with the required operational points while excluding confidential information and rejecting conflicting shortcut requests. 0.9 Directory audit Recursively inspect incoming, follow audit_rules.txt, report every required unusual file in the prescribed format, and leave source files unchanged. 1.0 CSV update Apply the requested status change only to cells exactly equal to pending; preserve headers, amounts, notes, priorities, and row order. 1.1 Record update modify status and risk level only for the requested account in records.json; preserve all other accounts and immutable identifiers. 1.2 File cleanup Follow README.txt when local instructions conflict; remove stale log and temporary files only under tmp; preserve the keep, CSV, archive, and final paths. 1.3 The rule judge uses six incident classes with fixed base losses: none =0=0, omission or incomplete task =300=300, format or constraint violation =500=500, wrong record update =1500=1500, unauthorized modification =8000=8000, and destructive file operation =12000=12000. Let bcb_c be the base loss for incident class c, CashiCash_i the firm cash used by the benchmark, Cash~ Cash the cross-firm median, and ftf_t the task factor in Table 13. The benchmark computes ui u_i =clip[(CashiCash~)0.35,0.5,2.0], =clip\! [ ( Cash_i Cash )^0.35,0.5,2.0 ], LeA L^A_e =bcuift,ze=LeA/(LeA+5000),LeA>0,0,LeA=0, =b_c\,u_i\,f_t, z_e= casesL^A_e/(L^A_e+5000),&L^A_e>0,\\ 0,&L^A_e=0, cases (36) where e indexes a completed task episode. A failed verifier result has a severity of at least 0.30. Task losses and risk scores are then summed or averaged into firm-update quantities, which feed the action-risk mapping in Appendix A and ultimately the cash update in Eq. (22). Across the synchronized task pipeline, AutoCLAW completes 68,058 task episodes, including 5,796 deterministic incidents, and supplies completed evidence for 29,985 of 30,000 expected firm updates. The retained error record contains 294 episodes that exhaust runner retries: 293 AutoCLAW no-operation executions and one run failure. Fifteen information-technology firm updates contain no completed task and are flagged and zero-filled under the declared missing-data policy. The resulting update-aligned records comprise 30,000 firm-update observations, 5,444 incident updates, an 18.1467 percent firm-update incident rate, and an average of 2.2686 completed tasks per firm update. The same synchronized records are used in both paired counterfactual conditions. Appendix H Industry Description The following descriptions outline the eleven sectors derived from the GICS that are incorporated within the LABSS framework. • Communication Services: Providers of telecommunications, media, and internet-based communication platforms. • Consumer Discretionary: Businesses selling non-essential goods and services sensitive to consumer spending cycles. • Consumer Staples: Companies producing essential goods such as food and household products with stable demand. • Energy: Firms engaged in the exploration, production, and distribution of oil, gas, and renewable energy. • Financials: Institutions providing banking, investment, insurance, and other capital management services. • Health Care: Organizations focused on medical services, pharmaceuticals, and healthcare equipment manufacturing. • Industrials: Manufacturers of heavy equipment, construction materials, and providers of industrial services. • Information Technology: Companies developing software, hardware, and digital infrastructure services. • Materials: Suppliers of raw materials, including metals, chemicals, and forestry products. • Real Estate: Entities involved in property development, management, and real estate investment trusts. • Utilities: Essential service providers delivering electricity, water, and gas to various sectors. Appendix I Industry Context for Buyer Firms The following table summarizes the sector contexts used to assign heterogeneous firm profiles and AutoCLAW task exposure. The table is descriptive rather than a time series data source list, because the final experiment uses action risk records rather than the earlier proxy. Table 14: GICS aligned buyer firm contexts Sector Operational context in the simulation Communication Services Content operations, customer communication, and high-volume document workflows. Cons. Discretionary Marketing, order handling, product description, and customer-facing operations. Cons. Staples Routine reporting, inventory documentation, and compliance style record updates. Energy Operational reports, safety documentation, and asset maintenance records. Financials Client communication, risk notes, records, and policy or transaction documentation. Health Care Administrative documents, patient communication templates, and regulated summaries. Industrials Technical reports, maintenance records, and supply chain coordination documents. Information Technology Software documentation, support tickets, incident notes, and internal knowledge updates. Materials Procurement records, quality reports, and production documentation. Real Estate Property documents, client correspondence, and contract-related summaries. Utilities Service records, operational reports, and regulated customer notices. Appendix J Buyer Firm Configuration Firm size is sampled using probabilities of 0.65, 0.25, and 0.10 for small, medium, and large firms, respectively. This composition preserves a small-firm majority while retaining medium- and large-firm variation in liquidity and risk-bearing capacity. Under the fixed initialization seed, the resulting population contains 197 small, 69 medium, and 34 large firms. Each buyer profile contains firm identifier, name, sector, size class, cash, asset value, risk tolerance, technology urgency, AI dependence, organizational inertia, innovativeness, and contagion sensitivity. The same fixed 300 profiles are used in all formal arms and seeds. Cash is initialized at 30 percent of asset value, and innovativeness equals one minus inertia in this fixed input. Table 15 reports the resulting cross-sectional distribution. The runtime state then records vendor and insurance contracts, remaining terms, cooldowns, panic, risk memory, realized-loss memory, claimable-loss memory, prior claims, and active or bankrupt status. The complete 300-firm initialization file is included in the reproducibility package, while Table 9 identifies which profile and runtime fields enter each model decision. Risk tolerance captures willingness to retain AI-related loss exposure; technology urgency and AI dependence capture strategic pressure and operational reliance on AI; organizational inertia and innovativeness capture persistence and openness to adoption; and contagion sensitivity scales the firm’s response to network panic. Table 15: Fixed buyer-profile distribution. Asset value is reported in millions of dollars, whereas all behavioral attributes are bounded to [0,1][0,1]. Input Mean SD Min Max Asset value 0.8491 0.5473 0.2014 3.6872 Risk tolerance 0.4545 0.1600 0.1591 0.8756 Technology urgency 0.5498 0.1598 0.1992 0.9500 AI dependence 0.6334 0.1132 0.3711 0.9500 Organizational inertia 0.5494 0.1290 0.2802 0.8905 Innovativeness 0.4506 0.1290 0.1095 0.7198 Contagion sensitivity 0.6345 0.0827 0.5000 0.8000