Modeling and pricing cybersecurity insurance with information asymmetry

Firms typically invest in security measures to reduce potential losses from cyber incidents. Since such measures cannot fully eliminate cyber risks, cyber insurance plays an important role in hedging residual losses. This paper studies contract design in a monopolistic cyber insurance market where policyholders differ in their underlying risk levels and choose unobservable security effort. We consider both risk-neutral and risk-averse agents and develop a theoretical framework to derive optimal insurance contracts and security investments. These contracts are designed to alleviate moral hazard and adverse selection under three information scenarios. The theoretical results reveal three main incentive effects: premium discounts promote security effort, more generous coverage weakens the incentive to protect, and protection generated by neighboring firms creates a substitution effect that weakens individual effort. Numerical experiments compare the optimal premium discount, coverage rate, security effort, and the insurer's expected payoff across the three information scenarios.