"Bonus hunger" behavior in the alternative bonus–malus system

In this article the "bonus hunger" behavior for the Alternative bonus–malus system (BMS) is discussed. The Alternative BMS is a model, where the next premium is the combination of the previous premium and the aggregate claim amount. The key characteristics for the comparison are the discounted premium reduction for some time horizon and the entire claim amount. Existence of the steady state for the BMS discussed in this paper was proved and the probability of claiming for the general model and for its steady state was found out.