A talk was given by the Head of the SDAT Education Department at the of the Statistics and its Aplications, Lisbon, Portugal under the title of "Bonus-Malus Systems: A Discussion of Some of the Problems". 

A Bonus-Malus System (BMS) is one of the ratemaking methods generally used in automobile insurance. BMS penalizes policyholders at faults for one or more claims by a premium surcharge, known as malus, and rewards the policyholders with a claim-free year by granting discount in the premium say bonus. An optimal BMS should be possibly fair for policyholders and financially balanced for the insurer. While much progress has been made on the development of BMS but for practical applications, many questions remain, including the reliability and efficiency of the systems. To deal with system efficiency ‘rigorously’ an open portfolio assumption must be considered. The approximation techniques proposed for this purpose are largely at a conceptual stage. In this talk, we categorize the existing BMS and then discuss the challenges in both theory and practice.