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On the Evaluation of the Asymptotic Fairness of Bonus-Malus Systems



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.

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  • Antonio José Heras Martínez & José Luis Vilar Zanón & José Antonio Gil Fana, 2001. "On the Evaluation of the Asymptotic Fairness of Bonus-Malus Systems," Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales 01-32, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
  • Handle: RePEc:ucm:doctra:01-32

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    1. Loimaranta, K., 1972. "Some asymptotic properties of bonus systems," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 6(03), pages 233-245, May.
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    Bonus-malus system; Asymptotic fairness; Goal Programming; Simplex method.;

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