Hostname: page-component-5c6d5d7d68-thh2z Total loading time: 0 Render date: 2024-08-21T19:02:39.701Z Has data issue: false hasContentIssue false
  • English
  • Français

Pareto Optimality and Equilibrium in an Insurance Market

Published online by Cambridge University Press:  17 April 2015

Alexey Y. Golubin
Alexey Y. Golubin*
Affiliation:
Russian Academy of Sciences, Design Information Technologies Center, Marshala Zhukova Street, 30-A Odintsovo, Moscow region, 143000 Russia, E-Mail: [email protected] [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The concept of economic equilibrium under uncertainty is applied to a model of insurance market where, in distinction to the classic Borch’s model of a reinsurance market, risk exchanges are allowed between the insurer and each insured only, not among insureds themselves. Conditions characterizing an equilibrium are found. A variant of the conditions, based on the Pareto optimality notion and involving risk aversion functions of the agents, is derived. An existence theorem is proved. Computation of the market premiums and optimal indemnities is illustrated by an example with exponential utility functions.

Keywords

Insurancepremiumindemnity functionPareto optimalityequilibrium
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 2 , November 2008 , pp. 441 - 459
Copyright
Copyright © ASTIN Bulletin 2008

References

Aase, K.K. (1993) Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization. ASTIN Bulletin 22, 185–211.CrossRefGoogle Scholar
Aase, K.K. (2002) Perspectives of Risk Sharing. Scand. Actuarial J. 2, 73–128.CrossRefGoogle Scholar
Borch, K. (1960) Reciprocal Reinsurance Treaties. ASTIN Bulletin 1, 171–191.CrossRefGoogle Scholar
Borch, K. (1962) Equilibrium in a Reinsurance Market. Econometrica 30, 424–444.CrossRefGoogle Scholar
Borch, K. (1990) Economics of Insurance. Edited by Aase, K.K. and Sandmo, A., Amsterdam, North-Holland.Google Scholar
Bühlmann, H. (1980) An Economic Premium Principle. ASTIN Bulletin 11, 52–60.CrossRefGoogle Scholar
Bühlmann, H. (1984) The General Economic Premium Principle. ASTIN Bulletin 14, 13–21.CrossRefGoogle Scholar
Gerber, H.U. (1978) Pareto-optimal Risk Exchanges and Related Decision Problems. ASTIN Bulletin 10, 25–33.CrossRefGoogle Scholar
Golubin, A.Y. (2005) Pareto-optimal Contracts in an Insurance Market. ASTIN Bulletin 35(2), 363–378.CrossRefGoogle Scholar
Golubin, A.Y. (2006) Pareto-optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value. Journal of Risk and Insurance 73, 469–487.CrossRefGoogle Scholar
Goovaerts, M.J., De Vylder, F. and Haezendonck, J. (1984) Insurance Premiums. Theory and Applications. Amsterdam, North-Holland.Google Scholar
Harker, P.T. and Pang, J.S. (1990) Finite-dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms and Applications. Mathematical Programming 48, 161–220.CrossRefGoogle Scholar
Lehmann, E.L. (1959) Testing Statistical Hypotheses. Wiley and Sons, New York.Google Scholar
Lemaire, J. (1990) 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
Mas-Collel, A. (1986) The Price Equilibrium Existence Problem in Topological Vector Lattices. Econometrica 54, 1039–1054.CrossRefGoogle Scholar
Tucker, H.G. (1967) A Graduate Course in Probability. Academic Press, New York.Google Scholar
Wyler, E. (1990) Pareto Optimal Risk Exchanges and a System of Differential Equations: A Duality Theorem. ASTIN Bulletin 20, 23–32.CrossRefGoogle Scholar