Optimum Insurance with Deviant Beliefs

Optimum insurance between a risk-neutral or risk-averse insurer and a risk-averse client has been widely studied under conditions of agreement about the distribution of probabilities of loss. The condition of agreement is relaxed here, and the client is assumed to be more optimistic than the insurer. When optimism is defined broadly, the optimum contracts can have almost any form and in general will not even resemble insurance contracts. However, the optimum contracts are insurance contracts under a condition that restricts the type of disagreement. Under the same condition, the optimum contract for a more optimistic client has a higher deductible than the optimum contract for a less optimistic one.