Dynamic optimal insurance and lack of commitment

This paper analyzes dynamic risk-sharing contracts between profit-maximizing insurers and risk-averse agents who face idiosyncratic income uncertainty and may self-insure through savings. We study Markov-perfect insurance contracts in which neither party can commit beyond the current period. We show that the limited commitment assumption on the insurer's side is only restrictive when he is endowed with a rate of return advantage and the agent has sufficiently large initial assets. In such a case, the consumption profile is distorted relative to the first-best. In a Markov-perfect equilibrium, the agent's asset holdings determine his period outside option and are thus, an integral part of insurance contracts, unlike the case when the insurer can commit. Whether the parties can contract on the agent's savings decisions or not affects the agreement as long as the insurer makes positive profits.