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Chains of Reinsurance Revisited

Published online by Cambridge University Press:  29 August 2014

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.

Type
Articles
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, 4348.Google Scholar
Lemaire, J. (1979) Reinsurance as a Cooperative Game. In Applied Game Theory, Physica-Verlag, Würzburg, 254269.CrossRefGoogle Scholar
Nash, J. (1950) The Bargaining Problem. Econometrica, 18 155162.CrossRefGoogle Scholar