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

• Autores: A. Heras, José Luis Vilar, José Antonio Gil Fana
• Localización: Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales, ISSN-e 2255-5471, Nº. 32, 2001, 38 págs.
• Idioma: inglés
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• Resumen

  • 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.