Optimal Insurance: Dual Utility, Random Losses, and Adverse Selection

We study a generalization of the classical monopoly insurance prob-lem under adverse selection (see Stiglitz 1977) where we allow for a random distribution of losses , possibly correlated with the agent's risk parameter that is private information. Our model explains pat-terns of observed customer behavior and predicts insurance con-tracts most often observed in practice: these consist of menus of several deductible-premium pairs or menus of insurance with cov-erage limits-premium pairs. A main departure from the classical insurance literature is obtained here by endowing the agents with risk-averse preferences that can be represented by a dual utility func-tional (Yaari 1987). (JEL D81, D82, D86, D91, G22)