Asymptotic Fairness of Bonus-Malus Systems and Optimal Scales of Premiums

A. Heras, J.L. Vilar and J.A. Gil
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A. Heras: Departamento de Economía Financiera y Actuarial, Universidad Complutense de Madrid, Spain
J.L. Vilar: Departamento de Economía Financiera y Contabilidad 1 (Economía Financiera y Actuarial), Facultad de Ciencias Económicas, UCM, Campus de Somosaguas, 28223 Pozuelo de Alarcón, Spain, e-mail: econ103@sis.ucm.es
J.A. Gil: Departamento de Economía Financiera y Actuarial, Universidad Complutense de Madrid, Spain

The Geneva Risk and Insurance Review, 2002, vol. 27, issue 1, 82 pages

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 system ability in assessing the individual risks in the long run. Firstly we define the asymptotic fairness of a bonus-malus system following an expression that can be found in J. Lemaire [1985]: Automobile Insurance. Actuarial Models. Dordrecht: Kluwer-Nijhoff Publishing, p. 168. Secondly, we define 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 Programming. The Geneva Papers on Risk and Insurance Theory (2002) 27, 61–82. doi:10.1023/A:1020633525146

Date: 2002
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