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

Antonio José Heras Martínez, José Luis Vilar Zanón and José Antonio Gil Fana
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Antonio José Heras Martínez: Departamento de Economía Financiera y Contabilidad I (Economía Financiera y Actuarial). Universidad Complutense de Madrid., https://www.ucm.es/economia-financiera-y-actuarial
José Luis Vilar Zanón: Departamento de Economía Financiera y Contabilidad I (Economía Financiera y Actuarial). Universidad Complutense de Madrid., https://www.ucm.es/economia-financiera-y-actuarial
José Antonio Gil Fana: Departamento de Economía Financiera y Contabilidad I (Economía Financiera y Actuarial). Universidad Complutense de Madrid., https://www.ucm.es/economia-financiera-y-actuarial

No 01-32, Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales

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.

Keywords: Bonus-malus system; Asymptotic fairness; Goal Programming; Simplex method. (search for similar items in EconPapers)
Pages: 38 pages
Date: 2001
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