%0 Report
%A Heras Martínez, Antonio José
%A Vilar Zanón, José Luis
%A Gil Fana, José Antonio
%T On the evaluation of the asymptotic fairness of bonus-malus systems
%J Documentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales
%D 2001
%@ 2255-5471
%U https://hdl.handle.net/20.500.14352/64429
%X 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.
%~