Aspects of Optimization in Automobile Insurance

Abstract

In most of the countries experience rating is used in automobile insurance. On the basis of a simple model the resulting credibility premiums — optimal in the sense of Bayesian estimators — are compared with the bonus-malus-classes of motor insurance in the FRG of today. The critical point in this approach is the knowledge of the structure function; this is exemplified by the german automobile insurance and its actual problems. Results without using a structure function are presented. To derive an optimal bonus-system within the framework of the model an heuristic procedure is evaluated. The last aspect of optimization deals with optimal bounds for the “bonus-hunger” which can be computed by means of dynamic-programming. For the special case of an exponential distribution for the amount of claims, the solution of this optimization is given by the solution of some Bernoulli differential equations.