Optimal Insurance : Dual Utility, Random Losses and Adverse Selection

We study a generalization of the classical monopoly insurance problem under adverse selection where we allow for a random distribution of losses, possibly correlated with the agent's risk parameter that is private information. Our main purpose is to provide a convenient analytic model that explains both the pattern of observed customer behavior and the pattern of insurance contracts most often observed in practice: these consist of menus of several deductible-premium pairs, or menus of insurance with coverage limits-premium pairs. The 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 functional