Heras Martínez, Antonio and Vilar Zanón, José Luis and Gil Fana, José Antonio (2001) On the evaluation of the asymptotic fairness of bonus-malus systems. [Working Paper or Technical Report]
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Official URL: http://eprints.ucm.es/6754/
Abstract
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. |
| Volume: | 2001 |
| Number: | 32 |
| ID Code: | 6754 |
| References: |
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: | 07 Dec 2011 14:42 |
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