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Calcul des Primes et Marchandage*

Published online by Cambridge University Press:  29 August 2014

Danielle Briegleb  and
Jean Lemaire
Danielle Briegleb
Affiliation:
Université Libre de Bruxelles
Jean Lemaire
Affiliation:
Université Libre de Bruxelles
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Two premium calculation principles by negotiation. Using, as main tools,

the classical risk exchange model by Borch and

the bargaining models of Nash and Kalai-Smorodinsky,

we define two new premium calculation principles, whose main goal is to take explicitly into account the attitude towards risk of the policy-holders. Those principles are neither additive nor iterative, but they nevertheless possess several important properties: the premium is translation-invariant, it does not depend neither on the reserves nor on the portfolio of the company; it takes into account all the moments of the claim distribution; it is independent of the policy-holder's wealth but increases with his risk aversion.

Coalition against an insurance company. While computing the core of this risk exchange, we show that it can be of the policy-holder's interest to coalize in order to obtain premium cuts.

Le modèle d'échange de risques de Borch entre plusieurs compagnies d'assurances soucieuses d'améliorer leur situation en formant un pool de réassurance a fait l'objet de très nombreuses publications. Ce n'est que depuis quelques années cependant que l'on semble s'être aperçu que le même modèle pouvait être utilisé pour décrire toute économie d'échange, en particulier le contrat d'assurance simple entre un assuré et sa compagnie. Si l'on suppose que les préférences de l'assuré peuvent être décrites par une fonction d'utilité exponentielle, et que l'assureur est indifférent au risque en première approximation, les contrats Pareto-optimaux consistent en une couverture complète du risque, moyennant le paiement d'une prime que le critère de Pareto-optimalité ne permet pas de déterminer.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 13 , Issue 2 , December 1982 , pp. 115 - 132
Copyright
Copyright © International Actuarial Association 1982

Footnotes

*

Presented at the 16th Astin Colloquium, September 27–30, 1982, Liège, Belgium.

References

BIBLIOGRAPHIE

Bardola, J. (1981) Optimaler Risikoaustausch als Anwendung für den Versicherungsvertrag. MVSV, 41–66.Google Scholar
Baton, B. et Lemaire, J. (1981) The Core of a Reinsurance Market. ASTIN Bulletin 12, 57–71.CrossRefGoogle Scholar
Borch, K. (1962) Equilibrium in a Reinsurance Market. Econometrica 30, 424–444.CrossRefGoogle Scholar
Bühlmann, H. et Jewell, W. (1979) Optimal Risk Exchanges. ASTIN Bulletin 10, 243–262.CrossRefGoogle Scholar
Gerber, H. (1974 a) On Additive Premium Calculation Principles. ASTIN Bulletin 7, 215–222.CrossRefGoogle Scholar
Gerber, H. (1974 b) On Iterative Premium Calculation Principles. MVSV, 163–172.Google Scholar
Gerber, H. (1978) Pareto-Optimal Risk Exchange and Related Decision Problems. ASTIN Bulletin 10, 25–33.CrossRefGoogle Scholar
Kalai, E. et Smorodinsky, M. (1975) Other Solutions to the Nash Bargaining Problem. Econometrica 43, 513–518.CrossRefGoogle Scholar
Leepin, P. (1975) Uber die Wahl von Nutzenfunktionen für die Bestimmung von Versicherungsprämien. MVSV, 27–45.Google Scholar
Lemaire, J. (1973) A New Concept of Value for Games Without Transferable Utilities. Int. J. of Game Theory 2, 205–214.CrossRefGoogle Scholar
Moffet, D. (1979) The Risk Sharing Problem. Geneva Papers 11, 5–13.Google Scholar
Nash, J. (1950) The Bargaining Problem. Econometrica 18, 155–162.CrossRefGoogle Scholar
Roth, A. (1980) Axiomatic Models of Bargaining. Springer.Google Scholar