The Efficiency of a Bonus-Malus System

The concept efficiency of a bonus-malus system was defined, apparently in a totally different way, consecutively by Loimaranta (I972) and Lemaire (1975, 1976). In this paper we start with a more general model that leads us to a definition of efficiency that contains both earlier ones as special cases. Further we introduce the definition of efficiency over a finite planning horizon and consider the efficiency not only for a single risk but also for the entire risk group. As a consequence of our approach we can also generalize the concepts excess premium and central value as they were introduced by Loimaranta.