THE PRACTICAL REPLACEMENT OF A BONUS-MALUS SYSTEM BY

In this paper we will show how to set up a practical bonus-malus system with a finite number of classes. We will use the actual claim amount and claims frequency distributions in order to predict the future observed claims fre-quency when the new bonus-malus system will be in use. The future observed claims frequency is used to set up an optimal bonus-malus system as well as the transient and stationary distributions of the drivers in the new bonus-malus system. When the number of classes as well as the transition rules of the new bonus-malus ystem have been adopted, the premium levels are obtained by minimizing a certain distance between the levels of the practical bonus-malus system and the corresponding optimal bonus-malus system. Some iterations are necessary in order to reach stabilization of the future observed claims frequency and the levels of the practical bonus-malus system. KEYWORDS Optimal bonus-malus system, practical bonus-malus system, hunger for bonus, observed claims frequency distribution, actual claims frequency distribution, iterative algorithm, Hofmann Distribution, non-parametric mixed Poisson fit. I