Insurance Fraud in a Rothschild–Stiglitz World

In this article, we model a competitive insurance market where policyholders privately have information about their probability of accident ex ante and know the state of the world ex post. We combine costly state verification without commitment and arguments from insurance contracting under adverse selection to characterize the resulting allocations. Insurance fraud convexifies the insurer's zero expected profit condition, which can lead to complete unraveling with low risks dropping out of the market. The standard case, however, involves rationing of low risks, which raises their probability of fraud and their success rate when committing it. As a result, adverse selection increases fraud in the economy. We also show that cross‐subsidization from low risks to high risks mitigates the fraud externality. Our results highlight that adverse selection and insurance fraud interact in nontrivial ways and have the potential to aggravate each other.