A SET OF BONUS-MALUS SYSTEMS FAIR BY TRANSITION RULES - ELEMENTS OF ANALYSIS

The paper considers a set of bonus-malus systems fair by transition rules (BMSF(TR)). Although the definition of such system reduces a set of all BM systems, the number of systems of BMSF(TR) type still remains huge. First the authors use a special algorithm to generate all possible systems of BMSF(TR) type with a given number of classes. Then they propose to implement a premium criterion that fulfils the definition of BMSF(TR) and, which is very important, makes systems financially balanced. Next they choose appropriate measures which allow to analyse and compare all possible systems of a given size in respect of their performance in different portfolios i.e. portfolios which differ by claim frequency and claim variance. The results of the analysis are general conclusions on how transition rules and portfolio's characteristics influence system performance.