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Pareto-optimal Contracts in an Insurance Market

Published online by Cambridge University Press:  17 April 2015

A.Y. Golubin
A.Y. Golubin*
Affiliation:
Dep. of Operations Research, Moscow Institute of Electronics and Mathematics, B. Trechsvjatitelsky per., 3/12, Moscow, 109028, Russia, E-mail: io@miem.edu.ru
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Abstract

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In distinction to the Borch’s model of a reinsurance market, this paper treats the problem of optimal risk exchange in an insurance market where treaties are allowed between the insurer and each insured only, not among insureds themselves. A characterization of the Pareto-optimal contract is found. It is shown that the indemnity function in the contract is of a coinsurance kind. We also present a way of finding Pareto-optimal contracts under individual rationality constraints. The obtained results are compared with those of the known model of risk exchange in a reinsurance market.

Keywords

Insurance contractPremiumIndemnity functionPareto optimalityIndividual rationality
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 2 , November 2005 , pp. 363 - 378
Copyright
Copyright © ASTIN Bulletin 2005

References

Aase, K.K. (2002) Perspectives of Risk Sharing. Scand. Actuarial J., 2, 73–128.CrossRefGoogle Scholar
Arrow, K. (1971) Essays in the Theory of Risk Bearing. Chicago, Markham.Google Scholar
Baton, B. and Lemaire, J. (1981) The Core of a Reinsurance Market. ASTIN Bulletin, 12, 57–71.CrossRefGoogle Scholar
Bazaraa, M. and Shetty, C. (1979) Nonlinear Programming. Theory and Algorithms. John Wiley, New York.Google Scholar
Borch, K. (1960a) Reciprocal Reinsurance Treaties. ASTIN Bulletin, 1, 171–191.CrossRefGoogle Scholar
Borch, K. (1960b) Reciprocal Reinsurance Treaties Seen as a Two-person Cooperative Game. Skand. Aktuarietidskrift, 43, 29–58.Google Scholar
Borch, K. (1990) Economics of Insurance. Edited by Aase K.K. and Sandmo A., Amsterdam, North-Holland.Google Scholar
Borm, P., Suijs, J. and Waeggenaere, A.D. (1998) Stochastic Cooperative Games in Insurance. Insurance: Mathematics and Economics, 22, 209–228.Google Scholar
Debreu, G. and Scarf, H. (1963) A Limit Theorem on the Core of an Economy. International Economic Review, 4, 235–246.CrossRefGoogle Scholar
Gerber, H.U. (1978) Pareto-optimal Risk Exchanges and Related Decision Problems. ASTIN Bulletin, 10, 25–33.CrossRefGoogle Scholar
Golubin, A.Y. (2002) Franchise Optimization in the Static Insurance Model. Journal of Mathematical Sciences, 112, 4126–4140.CrossRefGoogle Scholar
Golubin, A.Y. (2006) An Optimal Insurance Policy in the Individual Risk Model Seen as a Bargaining Game. Game Theory and Applications, 11, to appear.Google Scholar
Holmstrom, B. (1979) Moral Hazard and Observability. Bell Journal of Economics, 10, 74–91.CrossRefGoogle Scholar
Kalai, E. and Smorodinsky, M. (1975) Other Solutions to the Nash Bargaining Problem. Econometrica, 43, 513–518.CrossRefGoogle Scholar
Landsberger, M. and Meilijson, I. (1990) Lotteries, Insurance, and Star-shaped Utility Functions. Journal of Economic Theory, 52, 1–17.CrossRefGoogle Scholar
Lemaire, J. (1979) A Non Symmetrical Value For Games Without Transferable Utilities. Application to Reinsurance. ASTIN Bulletin, 10, 195–214.CrossRefGoogle Scholar
Lemaire, J. (1990a) Cooperative Game Theory and Its Insurance Applications. ASTIN Bulletin, 21, 17–40.CrossRefGoogle Scholar
Lemaire, J. (1990b) Borch’s Theorem. In: Louberge, H. (ed.) Risk, Information and Insurance. Essays in the Memory of Karl H. Borch, Kluwer Academic Publishers, Boston, London, 15–37.Google Scholar
Nash, J. (1950) The Bargaining Problem. Econometrica, 18, 155–162.CrossRefGoogle Scholar
Raviv, A. (1979) The Design of an Optimal Insurance Policy. The American Economic Review, 69, 84–96.Google Scholar
Tucker, H.G. (1967) A graduate course in probability. Academic Press, New York.Google Scholar
Wilson, R. (1968) The Theory of Syndicates. Econometrica, 36, 119–131.CrossRefGoogle Scholar
Wyler, E. (1990) Pareto Optimal Risk Exchanges and a System of Differential Equations: A Duality Theorem. ASTIN Bulletin, 20, 23–32.CrossRefGoogle Scholar