Insurance With Heterogeneous Preferences

Abstract

This paper studies an optimal insurance problem with finitely many potential policyholders. A monopolistic, risk-neutral insurer offers an insurance contract, and exponential utility maximizing individuals accept the offer or not. We allow for heterogeneity in the preferences of the individuals, while the insurer cannot discriminate in the insurance premium. We show that it is optimal for the insurer to offer only a full insurance contract, and the price optimization problem is reduced to a discrete problem, where the premium is an indifference premium for one individual in the market. Moreover, if individuals can self-select their insurance coverage given the market premium rate, then we find that partial insurance is generally optimal. Since the risk aversion parameters of individuals is generally unobserved, we also present a simulation-based framework. We show its convergence, and provide numerical examples.