Optimal Claim Decisions for a Bonus-Malus System: A Continuous Approach

For the premium calculation the insurer will split up his collectivity of risks into risk groups which are homogeneous with respect to some directly observable risk factors. All risks of such a risk group will be charged the same base premium. But it is clear that by such an a priori classification not all determined factors can be taken into consideration, so that there will still remain accident proneness differentials within a risk group. Since these differentials will be reflected in the course of time by the claim experience of each risk, the insurer can come to a fair tarification by adjusting, each period, the base premium according to the individual claim experience of the risk. Such a system in which earlier neglected risk factors are taken into account a posteriori is an individual experience rating system.