Sandra Pitrebois

Setting a bonus-malus scale in the presence of other rating factors: Taylor's work revisited

In this paper, we propose an analytic analogue to the simulation procedure described in Taylor (1997). We apply the formulas to a Belgian data set and discuss the interaction between a priori and a posteriori ratemakings.

An actuarial analysis of the French bonus-malus system

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 Prils algorithm for the convolution of independent and identically distributed random vectors.

How to transfer policyholders from one bonus-malus scale to the other ?

SummaryWith the deregulation of bonus-malus systems in the EU, it is important to obtain rules in order to transfer policyholders from one bonus-malus scale to another. The present paper proposes a solution to this problem.ZusammenfassungWegen der Deregulierung der Bonus-Malus Systeme in der EU ist es wichtig, Regeln für den Transfer eines Versicherungsnehmers von einem Bonus-Malus System in ein anderes aufzustellen. Der Artikel schlägt eine Lösung für dieses Problem vor.