Using Mixed Poisson Processes in Connection with Bonus-Malus Systems

For the construction of bonus-malus systems, we propose to show how to apply, thanks to simple mathematics, a parametric method encompassing those encountered in the literature. We also compare this parametric method with a non-parametric one that has not yet been used m the actuarial literature and that however permits a simple formulation of the stationary and transition probabilities in a portfolio whenever we have the intention to construct a bonus-malus system with finite number of classes KEYWORDS Mixed Poisson processes, non-parametric estimation, Hofmann's distribution, Bayes theorem, bonus-malus systems, stationary distribution.