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An actuarial analysis of the French bonus-malus system

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  • Sandra Pitrebois
  • Michel Denuit
  • Jean-François Walhin

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.

Suggested Citation

  • Sandra Pitrebois & Michel Denuit & Jean-François Walhin, 2006. "An actuarial analysis of the French bonus-malus system," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2006(5), pages 247-264.
  • Handle: RePEc:taf:sactxx:v:2006:y:2006:i:5:p:247-264
    DOI: 10.1080/03461230600986136
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