Optimal Insurance under Heterogeneous Belief

Abstract

In this paper, we study an optimal insurance problem, which allows the insured and the insurer to have heterogeneous probability beliefs in the distribution of potential losses, on the basis of which we maximize the expected utility of the insured’s final wealth. In order to reduce ex-post moral hazard, we assume that the alternative insurance contract follows the principle of indemnity and incentive compatibility constraints. Under the assumption of Wang’s premium principle, we derive a necessary and sufficient condition for the optimal solution. Then we discuss some particular characteristics of the optimal solution and the optimality of no insurance and full insurance.