Exponential Bonus-Malus Systems Integrating A Priori Risk Classifications

The paper contains a brief review of the bonus/malus ratemaking methodology found within the European community. It proceeds to explain how, under such systems, a priori and a posteriori ratemaking have to be integrated into a continuous risk evaluation mechanism. Loss functions that are applicable to the analysis are introduced. Methods that are developed in the paper are then shown by an example using a portfolio of business from a Spanish insurer. Vehicle power, driver age, and driving record are all combined together within the analysis. It is ultimately shown that the (pre-judged) good risks are already rewarded in their base premiums, and consequently require a smaller bonus (i.e. premium reduction) following an accident-free period than do the risks that had been pre-judged as bad risks.