Dynamic Optimal Insurance and Lack of Commitment

FRB of St. Louis Working Paper No. 2011-029C

27 Pages Posted: 13 Apr 2012 Last revised: 11 Jul 2013

See all articles by Alexander Karaivanov

Alexander Karaivanov

Simon Fraser University (SFU) - Department of Economics

Fernando M. Martin

Federal Reserve Banks - Federal Reserve Bank of St. Louis

Date Written: July 1, 2013

Abstract

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.

Keywords: Optimal insurance, lack of commitment, Markov-perfect equilibrium, asset contractibility

JEL Classification: D11, E21

Suggested Citation

Karaivanov, Alexander and Martin, Fernando M., Dynamic Optimal Insurance and Lack of Commitment (July 1, 2013). FRB of St. Louis Working Paper No. 2011-029C. Available at SSRN: https://ssrn.com/abstract=2038953 or http://dx.doi.org/10.2139/ssrn.2038953

Alexander Karaivanov (Contact Author)

Simon Fraser University (SFU) - Department of Economics ( email )

8888 University Drive
Burnaby, British Columbia V5A 1S6
Canada

Fernando M. Martin

Federal Reserve Banks - Federal Reserve Bank of St. Louis ( email )

411 Locust St
Saint Louis, MO 63011
United States
314-444-7350 (Phone)

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