Optimal Insurance Contracts with Limited Commitment and Unobservable Disability

Abstract

We study a continuous-time model of an optimal long-term labor contract with a randomly arriving disability shock under two frictions: the agent cannot commit to a long-term contract and can falsely claim disability. We provide the explicit solution and analyze the optimal contract by using an optimal stopping approach. We show that the optimal contract can be implemented under a three-account trading system, which has different features from systems in the literature that are generated under only one of the two frictions. By using the three-account system, we investigate how the arrival intensity of the disability shock and the level of disability severity have an impact on the optimal contract. Finally, we also perform a quantitative analysis on the firm’s cost from providing inefficient contracts caused by the current long-term disability insurance practice.