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The Core of a Reinsurance Market*

Published online by Cambridge University Press:  29 August 2014

Bernard Baton  and
Jean Lemaire
Bernard Baton
Affiliation:
Université Libre de Bruxelles
Jean Lemaire
Affiliation:
Université Libre de Bruxelles
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Abstract

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In a series of celebrated papers, K. Borch characterized the set of the Pareto-optimal risk exchange treaties in a reinsurance market. However, the Pareto-optimality and the individual rationality conditions, considered by Borch, do not preclude the possibility that a coalition of companies might be better off by seceding from the whole group. In this paper, we introduce this collective rationality condition and characterize the core of this game without transferable utilities in the important special case of exponential utilities. The mathematical conditions we obtain can be interpreted in terms of insurance premiums, calculated by means of the zero-utility premium calculation principle. We then show that the core is always non-void and conclude by an example.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 12 , Issue 1 , June 1981 , pp. 57 - 71
Copyright
Copyright © International Actuarial Association 1981

Footnotes

*

This paper was greatly improved after successive presentations at the Eidgenössische Technische Hochschule in Zürich, the University of California at Berkeley and the Oberwolfach Meeting on Risk Theory.

References

Borch, K. (1960a). Reciprocal reinsurance treaties seen as a two-person cooperative game. Skandinavisk Aktuarietidskrift 43, 29–58.Google Scholar
Borch, K. (1960b). Reciprocal reinsurance treaties. Astin Bulletin 1, 170–191.CrossRefGoogle Scholar
Bönen, K. (1961). The utility concept applied to the theory of insurance. Astin Bulletin 1, 245–255.Google Scholar
Borch, K. (1962). Equilibrium in a reinsurance market. Econometrics. 30, 424–444.CrossRefGoogle Scholar
Bühlmann, H. (1970). Mathematical methods in risk theory. Springer-Verlag, Berlin.Google Scholar
Du Mouchel, W. (1968). The Pareto-optimality of an n-company reinsurance treaty. Shandinavisk Akluarietidskrift 51, 165–170.Google Scholar
Gerber, H. (1974a). On additive premium calculation principles. Astin Bulletin!, 215–222.Google Scholar
Gerber, H. (1974b). On iterative premium calculation principles. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker 74, 163–172.Google Scholar
Leepin, P. (1975). Über die Wahl von Nutzenfunktioncn für die Bestimmung von Versicherungsprämien. Mitteilungen der Vereinigung Schweizerischer Versicherungs-mathematiker 75, 27–45.Google Scholar
Lemaire, J. (1973). Optimalité d'un contrat d'échange de risques entre assureurs. Cahiers du C.E.R.O. 15, 139–156.Google Scholar
Lemaire, J. (1979). A non-symmetrical value for games without transferable utilities, application to reinsurance. Astin Bulletin 10, 195–214.CrossRefGoogle Scholar