Models of insurance fraud: Build-up, ex post moral hazard and optimal contracts

This dissertation studies the problem of insurance fraud using a game theoretic model where a policyholder and an insurer play non-cooperatively. The model is based on the traditional costly state verification framework where the policyholder has private information concerning the state of the world (his loss), and must report it to the insurer. The insurer can learn what the state of the world is by incurring an audit cost. This information asymmetry result in what is called ex post moral hazard. The traditional way to solve this problem is for the insurer to commit to an auditing strategy. This dissertation innovates by removing the insurer\u27s ability to commit. The models in my dissertation are best described as part of the Costly State Verification-Stochastic Auditing-Discrete States-No Commitment literature. I study two types of insurance claim fraud: fraud build-up and auto-theft fraud. In insurance fraud build-up, I assume that the occurrence of an accident is common knowledge. What is known only to the policyholder is the severity of the accident. In auto-theft fraud, I assume that the occurrence of an accident is known to the policyholder only. The possible loss, however, is unique. The optimal contract is such that the policyholder is more than fully insured in the high loss state. In case of auto-theft fraud, this means that the unique possible loss is overcompensated. In the case of build-up, assuming a two-point distribution of losses, the policyholder receives more than the amount he lost if the loss is high. Surprisingly, the penalty inflicted to those who were caught committing fraud has no impact on the optimal contract. Concentrating on the case of build-up, I also find that the policyholder receives the same expected marginal utility in the accident state as in the no-accident state; this is true in the two-point build-up as in the T-point build up cases. This has the interesting policy implication that in order to reduce the amount of insurance fraud in the economy, insurers should be allowed to overcompensate policyholders for their loss