The Insurer's Dilemma

Insurance is the obvious way to move delegation risk off a principal’s books, and it creates a second delegation problem. Once Alice is insured against Bob’s failures, her insurer has to trust Alice. It must trust her to keep supervising Bob after the loss is no longer hers (moral hazard), and to be the kind of client she says she is (adverse selection). Economics worked out much of this between the 1960s and 1970s. Two real markets show the results in use: fidelity insurance, which has priced employee dishonesty for a long time, and AI liability insurance, a niche product since 2018 that became a visible market, and a target of exclusions, in 2025–26.

The framework in principal–agent terms

This site’s vocabulary maps onto the principal–agent literature as follows.

This site	Economics	Source
Delegation risk left after controls	Residual loss: the agent’s divergence that monitoring and bonding do not prevent	Jensen & Meckling 1976
Delegation risk + verification spend + bond costs	Agency cost = monitoring + bonding + residual loss	Jensen & Meckling 1976
Defection	Moral hazard (hidden action): the agent’s unobserved choices diverge from the principal’s interest	Arrow 1963; Pauly 1968; Holmström 1979
Verification and monitoring	Monitoring. The informativeness principle: a contract should use any signal that carries information about the agent’s action	Holmström 1979
Bond	Bonding cost, borne by the agent to make its commitment credible	Jensen & Meckling 1976
Deductibles and partial coverage	Optimal partial insurance under moral hazard	Pauly 1968; Shavell 1979
Clients the insurer cannot tell apart	Adverse selection, and screening by menus of contracts	Rothschild & Stiglitz 1976
Ambiguity loading	Ambiguity aversion in insurance pricing	Hogarth & Kunreuther 1989

The hijack channel, a third party steering the delegate, has no counterpart here. It is closer to the external crime that crime and cyber policies cover, such as social engineering and funds-transfer fraud.

Moral hazard: why full coverage fails

If Alice is fully insured against Bob, she loses her reason to choose him carefully, to supervise him, or to act on warning signs. Arrow (1963) analyzed the problem for medical insurance. Pauly (1968) showed that once insurance changes behavior, full coverage need not be optimal. Shavell (1979) worked out the contract. When the insurer cannot observe the insured’s care, the best policy leaves the insured bearing part of the loss. When it can observe care, it can tie the premium to care and offer fuller coverage.

That gives three standard ways to keep the principal’s incentive alive:

• Deductible. Alice pays the first part of any loss. She stays careful about small losses, but her incentive weakens beyond the deductible.
• Co-insurance. Alice pays a fixed share of every loss, so every dollar lost costs her something.
• Cap. Cover stops at a limit. Alice keeps the catastrophic tail, and with it an incentive to prevent catastrophes.

There is also a substitute for all three: monitoring. If the insurer can see that Alice supervises Bob, through audits, reports or access to logs, it needs less of her money at risk to keep her careful. Holmström’s informativeness principle says why: a signal that carries information about her effort beyond what the insurer already observes improves the contract.

Adverse selection: why pools unravel

Insurers cannot see everything their clients know. The clients keenest to buy delegation cover are disproportionately the ones who expect to claim. A premium set for the average client drives away the careful ones. That raises the average risk, which raises the premium again. Rothschild and Stiglitz (1976) showed that under this kind of hidden information, a competitive market has no equilibrium in which both kinds of client buy the same policy, and sometimes no equilibrium at all. Insurers instead offer menus that make clients reveal their type, such as a cheap, high-deductible policy that only confident clients choose. Underwriting questionnaires, waiting periods, exclusions for prior losses and discounts for documented controls are the working versions.

Correlated losses and the limits of insurability

The worst case cuts both ways. When a delegate could cause a loss far larger than the principal’s capital, the principal most needs cover, and the insurer most needs the principal to be careful. A cap resolves this by leaving the catastrophic tail with the principal, which is exactly where the principal wanted protection.

Insurers face a second tail problem, across their portfolio. Berliner (1982) proposed nine criteria for insurability, grouped as actuarial, market and societal conditions. The actuarial ones bind here: losses must be independent across policies with estimable probabilities, and the maximum possible loss must be bearable for the insurer. Correlation breaks both. It matters because an insurer holds capital against a tail measure of its whole portfolio, not against expected loss, and expected losses add regardless of correlation while tail measures do not (Risk Budgeting and Tail Measures). Ibragimov, Jaffee and Walden (2009) show that when losses are heavy-tailed and insurers have limited liability, insurers may rationally decline to cover a risk even when the market as a whole could share it, a “nondiversification trap”. Cyber risk is the nearest precedent. Biener, Eling and Wirfs (2015) applied Berliner’s criteria to 994 cyber losses from an operational-risk database. They found highly interrelated losses, scarce data, a fast-changing risk and severe information asymmetry, and noted that insurers responded to the uncertainty with high deductibles and low limits. The same problems hold back AI cover.

Even human dishonesty is not independent across policies: Dionne and Wang (2013) find that the severity of fraud in Taiwan’s auto-theft insurance market is countercyclical. AI makes correlation much worse. If many clients delegate to the same model, one failure can produce thousands of simultaneous claims. That is the entanglement tax at the scale of a market.

What real markets do

Fidelity and crime insurance

Fidelity bonds and commercial crime policies cover theft and fraud by employees, the defection channel for human delegates. The underlying losses are well measured. The Association of Certified Fraud Examiners’ Occupational Fraud 2024: A Report to the Nations analyzes 1,921 cases from 138 countries and territories. The median loss was $145,000 and the median fraud ran 12 months before detection, most often by a tip (43% of cases). Frauds by owners and executives had a median loss of $500,000, against $60,000 for staff-level employees. 57% of victims recovered nothing. Each of the 18 anti-fraud controls studied was associated with both faster detection and lower losses.

The policies follow the theory. Standard crime forms exclude theft by the insured itself, and by employees the insured already knew to be dishonest. Coverage for an employee ends once a dishonest act is discovered. Underwriting asks about internal controls such as segregation of duties and audits. The owner exclusion is the Ouroboros case: when the insured controls the loss, no premium is fair.

A premium is not exposure, and it is not delegation risk either. It is the insurer’s estimate of expected loss plus loadings for expenses, capital, profit and ambiguity, so the insurer’s expected loss sits below the premium. Read a fidelity premium as an upper estimate of the market’s view of a delegate’s defection risk.

AI liability insurance

By late 2026 the market moves in two directions. Specialist products cover AI failures affirmatively, while mainstream insurers write them out of existing policies.

Affirmative cover:

• Munich Re has insured AI performance failures since 2018. Its aiSure products back AI vendors’ performance warranties and cover companies using AI against losses from AI errors, such as lost revenue, business interruption and legal damages.
• Armilla, a Lloyd’s coverholder, launched an AI liability policy in April 2025, underwritten at Lloyd’s by underwriters including Chaucer. It responds when an AI system fails to perform as intended.
• The Artificial Intelligence Underwriting Company (AIUC) launched in July 2025 with a $15 million seed round. It combines a standard for AI agents (AIUC-1, built on the NIST AI RMF, the EU AI Act and MITRE ATLAS), audits against it, and insurance whose price and availability depend on the audit. In February 2026 ElevenLabs reported that its voice agents had been certified against AIUC-1 after 5,835 tests across 14 risk categories, making them eligible for an AIUC-1-backed policy.

Exclusions:

• In November 2025 the Financial Times reported that W. R. Berkley, Great American and Chubb had asked US state regulators to approve exclusions for AI-related liability in corporate policies. The reasons given were opacity (model outputs are “too much of a black box”) and systemic risk. An Aon executive noted that insurers can absorb a $400 million loss at one company; TechCrunch’s gloss was that they cannot absorb an agentic failure that causes 10,000 losses at once.
• Verisk’s ISO, which drafts the standard US policy forms, introduced optional generative-AI exclusion endorsements for commercial general liability, effective January 2026 (Independent Agent). CG 40 47 excludes bodily injury, property damage, and personal and advertising injury arising from generative AI. CG 40 48 excludes only the last. CG 35 08 excludes bodily injury and property damage under products and completed-operations cover.

Both movements fit the theory. Where the insurer can audit, as AIUC does, monitoring substitutes for retention and cover is offered. Where losses are correlated across policyholders or the system is opaque, insurers exclude the risk rather than price it. These are the first market prices for AI delegation risk. The affirmative market is small, its loss history is short and its prices are not public, so there is no evidence yet on whether the prices are accurate.

Where insurance stops working: adversarial agents

All of this assumes that the party whose behavior the contract shapes is the party that controls the loss. In the moral-hazard model that party is the insured principal, and partial coverage keeps her careful. A scheming delegate breaks the assumption. Its behavior does not depend on Alice’s coverage ratio. It may also corrupt the signals that monitoring relies on, and the informativeness principle helps only while a signal is informative about what the agent actually did. Monitors can fail strategically as well. Mookherjee and Png (1995) model a bribable pollution inspector, and find that because inspector and factory interact strategically, raising the penalty for corruption can increase pollution.

Against such an agent, coverage terms do not reduce risk. They only decide who bears the loss. What reduces it is constraining what the agent can do, with a hard exposure envelope, and monitoring it cannot falsify, with ledger inputs measured at the boundary. Any claim that those constraints hold against intentional subversion needs a control evaluation (Greenblatt et al. 2023). Insurance can price a delegation that is already bounded. It cannot bound one.

References

• Arrow, K. J. (1963). Uncertainty and the Welfare Economics of Medical Care. American Economic Review 53(5), 941–973.
• Association of Certified Fraud Examiners (2024). Occupational Fraud 2024: A Report to the Nations.
• Berliner, B. (1982). Limits of Insurability of Risks. Prentice-Hall.
• Biener, C., Eling, M., & Wirfs, J. H. (2015). Insurability of Cyber Risk: An Empirical Analysis. Geneva Papers on Risk and Insurance – Issues and Practice 40(1), 131–158.
• Dionne, G., & Wang, K. C. (2013). Does Insurance Fraud in Automobile Theft Insurance Fluctuate with the Business Cycle? Journal of Risk and Uncertainty 47(1), 67–92.
• Greenblatt, R., Shlegeris, B., Sachan, K., & Roger, F. (2023). AI Control: Improving Safety Despite Intentional Subversion. ICML 2024.
• Hogarth, R. M., & Kunreuther, H. (1989). Risk, Ambiguity, and Insurance. Journal of Risk and Uncertainty 2(1), 5–35.
• Holmström, B. (1979). Moral Hazard and Observability. Bell Journal of Economics 10(1), 74–91.
• Ibragimov, R., Jaffee, D., & Walden, J. (2009). Nondiversification Traps in Catastrophe Insurance Markets. Review of Financial Studies 22(3), 959–993.
• Jensen, M. C., & Meckling, W. H. (1976). Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure. Journal of Financial Economics 3(4), 305–360.
• Mookherjee, D., & Png, I. P. L. (1995). Corruptible Law Enforcers: How Should They Be Compensated? Economic Journal 105(428), 145–159.
• Pauly, M. V. (1968). The Economics of Moral Hazard: Comment. American Economic Review 58(3), 531–537.
• Rothschild, M., & Stiglitz, J. (1976). Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information. Quarterly Journal of Economics 90(4), 629–649.
• Shavell, S. (1979). On Moral Hazard and Insurance. Quarterly Journal of Economics 93(4), 541–562.

See also Delegation Accounting for the balance-sheet view and the ambiguity loading.