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Distributions stationnaires d'un système bonus–malus et probabilité de ruine

Published online by Cambridge University Press:  29 August 2014

Par François Dufresne
Par François Dufresne*
Affiliation:
Université de Lausanne
*
Ecole des HEC, Université de Lausanne, CH-1015 Lausanne, Switzerland.
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Abstract

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It is shown how the stationary distributions of a bonus–malus system can be computed recursively. It is further shown that there is an intrinsic relationship between such a stationary distribution and the probability of ruin in the risk-theoretical model. The recursive algorithm is applied to the Swiss bonus–malus system for automobile third-party liability and can be used to evaluate ruin probabilities.

Keywords

Bonus–malusstationary distributionsprobability of ruin
Type
Prize-Winning Papers of the ASTIN Competition 1987
Information
ASTIN Bulletin: The Journal of the IAA , Volume 18 , Issue 1 , April 1988 , pp. 31 - 46
Copyright
Copyright © International Actuarial Association 1988

References

Bibliographie

Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. et Nesbitt, C. J. (1987) Actuarial Mathematics. Society of Actuaries, Chicago.Google Scholar
Cox, D. R. et Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, Londres.Google Scholar
Dickson, D. C. M. et Gray, J. R. (1984) Exact solutions for ruin probability in the presence of an absorbing upper barrier. Scandinavian Actuarial Journal 3, 174–186.CrossRefGoogle Scholar
Filler, W. (1966) An Introduction to Probability Theory and its Applications, 2è éd. Wiley, New York.Google Scholar
Giezendanner, E., Straub, E. et Wettenschwiler, K. (1972) Zur Berechnung von Ruinwarscheinlichkeiten. Transactions of the 19th International Congress of Actuaries: Oslo.Google Scholar
Karlin, S. et Taylor, H. M. (1975) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
Lemaire, J. (1985) Automobile Insurance: Actuarial Models. Kluwer, Amsterdam.CrossRefGoogle Scholar
Lemaire, J. (1982) L'assurance automobile: problèmes. Labor, Bruxelles.Google Scholar
Lindley, D. V. (1952) The theory of queues with a single server. Proceedings of the Cambridge Philosophical Society 48, 277–289.CrossRefGoogle Scholar
Loimaranta, K. (1972) Some asymptotic properties of bonus systems, ASTIN Bulletin 6, 233–245.CrossRefGoogle Scholar
Seal, H. L. (1969) Stochastic Theory of a Risk Business. Wiley, New York.Google Scholar
Vepsäläinen, S. (1972) Applications to a theory of bonus systems. ASTIN Bulletin 6, 212–221.CrossRefGoogle Scholar