An actuarial analysis of the French bonus-malus system

Sandra Pitrebois, Michel Denuit and Jean-François Walhin

Scandinavian Actuarial Journal, 2006, vol. 2006, issue 5, 247-264

Abstract: The bonus-malus system in force in France differs from most of those used in industrialized countries around the world. Policyholders do not move inside a scale but their premium is obtained with the help of multiplicative CRM coefficients (CRM stands for the acronym of the French coefficient de réduction-majoration). The French bonus-malus system has been the topic of very few scientific investigations in the actuarial literature. This paper purposes to analyze this bonus-malus system in details. Despite its apparent simplicity, it will be seen that it leads to nontrivial mathematical problems. The financial equilibrium of the bonus-malus system is also investigated thanks to the multivariate De Pril's algorithm for the convolution of independent and identically distributed random vectors.

Date: 2006
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DOI: 10.1080/03461230600986136

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