Can Bonus‐Malus Allieviate Insurance Fraud?

Traditionally, insurance companies attempt to reduce (or even eliminate) fraud via audit strategies under which claims may be investigated at some cost to the insurer, with a penalty imposed upon insureds who are found to report claims fraudulently. However, it is also clear that, in a multiperiod setting, bonus‐malus contracts (increases in subsequent premiums whenever a claim is presented) also provide an incentive against fraud. In this article, we consider a model in which, conditional upon the client renewing his contract, the only mechanism used to combat fraud is bonus‐malus. In this way, our model provides the opposite pole to the pure audit model. We show that in our simplified setting there exists a bonus‐malus contract that will eliminate all fraud in all periods, while guaranteeing nonnegative expected profits to the insurer and participation by the insured. We also consider the dynamics of the solution, the effect of an increase in risk aversion on the solution, and the welfare implications.