Insurance Contracting with the Coexistence of Adverse Selection and Moral Hazard

Abstract

The asymmetric information problem has been widely discussed in the context of insurance markets. Most of previous research usually treats adverse selection and moral hazard separately, though it is quite possible that they may coexist and interact with each other. In this paper, we build a principal-agent model to examine optimal contracts in a competitive insurance market facing adverse selection and moral hazard simultaneously. We apply the change-of-variable method and the Kuhn-Tucker conditions to solve the optimization programs and find that there are several forms of separating Nash equilibria, although separating Nash equilibria may not exist. Our model brings richer equilibria and retains some properties in the benchmark models of pure adverse selection and pure moral hazard. For example, no agent is offered full insurance, and the positive correlation between insurance coverage and risk type still holds. Our study on comparative statics indicates that, under some conditions, the optimal indemnity and premium, in general, decrease with the disutility, increase with the potential loss and decrease with the intial wealth of the insured.

Keywords: Insurance Contract, Adverse Selection, Moral Hazard