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Dynamic Optimal Insurance and Lack of Commitment

We analyze dynamic risk-sharing contracts between profit-maximizing insurers and risk-averse agents who face idiosyncratic income uncertainty and can 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 restrictive only when he is endowed with a rate of return advantage and the agent has sufficiently large initial assets. In such a case, the agent''''''''s consumption profile is distorted relative to the first-best. In a Markov-perfect equilibrium, the agent''''''''s asset holdings determine his outside option each period and are thus an integral part of insurance contracts, unlike when the insurer can commit long-term. Whether the parties can contract on the agent''''''''s savings decision affects the Markov-perfect contract as long as the insurer makes positive profits.

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