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

Author

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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)

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

Suggested Citation

  • A. Heras & J.L. Vilar & J.A. Gil, 2002. "Asymptotic Fairness of Bonus-Malus Systems and Optimal Scales of Premiums," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 27(1), pages 61-82, June.
    • Handle: RePEc:pal:genrir:v:27:y:2002:i:1:p:61-82
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    Cited by:

    1. Pablo J. Villacorta & Laura González-Vila Puchades & Jorge de Andrés-Sánchez, 2021. "Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance," Mathematics, MDPI, vol. 9(4), pages 1-23, February.

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