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On the evaluation of the asymptotic fairness of bonus-malus systems

Heras Martínez, Antonio José and Vilar Zanón, José Luis and Gil Fana, José Antonio (2001) On the evaluation of the asymptotic fairness of bonus-malus systems. [ Documentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales; nº 32, 2001, ISSN: 2255-5471 ]

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In this paper we try to evaluate the asymptotic fairness of bonus-malus systems, assuming the simplest case when there is no hunger for bonus.The asymptotic fairness has to be understood as the bonus-malus systemability in assessing the individual risks in the long run (see Lemaire[1995] p.xvi). Firstly we de…ne the asymptotic fairness of a bonus-malussystem following an expression that can be found in Lemaire [1985] p.168. Secondly, we de…ne a measure of the global asymptotic fairness considering the structure function of the risk group. Finally we try to calculate, for each set of transition rules and a given structure function,the scale of premiums that brings the global asymptotic fairness closest to the ideal situation where each insured pays in the long run a premium corresponding to its own claim frequency. This is possible thanks to the application of a multiobjective optimization technique named Goal Programing. We give an example illustrating the fact that the ideal case could be fairly well approached.

Item Type:Working Paper or Technical Report
Uncontrolled Keywords:Bonus-malus system; Asymptotic fairness; Goal Programming; Simplex method.
Subjects:Social sciences > Economics > Money
Series Name:Documentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales
ID Code:6754

DE PRIL, N. [1978]: The E¢ciency of a Bonus-Malus System. ASTIN Bulletin, no10, 59-72.

KEMENY, J.G. and SNELL, J.L. [1976]: Finite Markov Chains. Springer-Verlag.

KLUGMAN, S.A. and PANJER, H.H. andWILLMOT, G.E. [1998]: Loss Models. From Data to Decisions. Wiley series in Probability and Statistics.

LEMAIRE, J. [1985]: Automobile Insurance. Actuarial Models. Kluwer-Nijho¤ Publishing.

LEMAIRE, J. [1995]: Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers.

LEMAIRE, J. [1998]: Bonus-Malus System: the European and Asian Approach to Merit-Rating. North American Actuarial Journal. Volume 2, Number 1.

LOIMARANTA, K. [1972]: Some Asymptotic Properties of Bonus Systems. ASTIN Bulletin, 6, 233-245.

NORBERG, R. [1976]: A Credibility Theory for Automobile Bonus Systems. Scandinavian Actuarial Journal, 92-107.

PESONEN, M. [1963]: A Numerical Method of Finding a Suitable Bonus Scale. ASTIN Bulletin 2, 102-108.

ROMERO, C. [1991]: Handbook of Critical Issues in Goal Programming. Pergamon Press, Oxford.

ROMERO, C. [1993]: Teoría de la Decisión Multicriterio: Conceptos, Técnicas y Aplicaciones. Alianza Universidad Textos, Madrid.

VILAR, J.L. [2000]: Arithmetization of Distributions and Linear Goal Programming. Insurance: Mathematics and Economics 27, 113-122.

Deposited On:30 Nov 2007
Last Modified:02 Jun 2015 10:55

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