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Chains of Reinsurance Revisited

Published online by Cambridge University Press:  29 August 2014

Jean Lemaire  and
Jean-Pierre Quairiere
Jean Lemaire*
Affiliation:
Université Libre de Bruxelles, Belgium
Jean-Pierre Quairiere*
Affiliation:
Université Libre de Bruxelles, Belgium
*
Université Libre de Bruxelles, Institut de Statistique, C.P. 210, 50 Boulevard du Triomphe B-1050 Bruxelles.
Université Libre de Bruxelles, Institut de Statistique, C.P. 210, 50 Boulevard du Triomphe B-1050 Bruxelles.
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Abstract

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Chains of reinsurance were first modelled by Gerber, in a special case. It is shown that more general results can be obtained by applying Borch's theorem. The Pareto-optimal reinsurance indemnities are uniquely determined using the only assumption that the participating companies use exponential utility functions. A simple comparison then shows that Gerber's indemnities are not Pareto-optimal. Even if no assumption at all is introduced, the indemnities are shown to be closely linked to the risk aversions of the participants.

Keywords

Reinsurancerisk exchangebargaining theory
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue 2 , November 1986 , pp. 77 - 88
Copyright
Copyright © International Actuarial Association 1986

References

Borch, K. (1985) Some Comments on the Paper: Chains of Reinsurance: Non-Cooperative Equilibria and Pareto-Optimality. 12th Seminar of the European Group of Insurance Economics, Geneva Association.Google Scholar
Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer-Verlag: Berlin.Google Scholar
Gerber, H. (1984) Chains of Reinsurance. Insurance: Mathematics and Economics, 3, 43–48.Google Scholar
Lemaire, J. (1979) Reinsurance as a Cooperative Game. In Applied Game Theory, Physica-Verlag, Würzburg, 254–269.CrossRefGoogle Scholar
Nash, J. (1950) The Bargaining Problem. Econometrica, 18 155–162.CrossRefGoogle Scholar