Asymptotic Fairness of Bonus-Malus Systems and Optimal Scales of Premiums
Source: The GENEVA PAPERS on Risk and Insurance Theory, Volume 27, Number 1, June 2002 , pp. 61-82(22)
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 : 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.
Document Type: Research Article
Affiliations: 1: Departamento de Economía Financiera y Actuarial, Universidad Complutense de Madrid, Spain 2: Departamento de Economía Financiera y Contabilidad 1 (Economía Financiera y Actuarial), Facultad de Ciencias Económicas, UCM, Campus de Somosaguas, 28223 Pozuelo de Alarcón, Spain. email@example.com
Publication date: June 1, 2002