An alternative model for bonus-malus system

The paper introduces an alternative approach to the bonus-malus system construction. In the presented model the premium calculation is based on the previous premium and on the claim severity component as well. Following to the concept of an optimal bonus-malus system the necessary and sufficient condition for the aggregate premiums to be a martingale series have been found out. Thus the presented approach differs totally from the usual bonus-malus classes as well as from the systems, where the severity of the claim is omitted.