Varying transition rules in bonus-malus systems

from rules specification to determination of optimal relativities

Research output: Contribution to journalArticle

5 Citations (Scopus)


In this paper, we extend the proposed idea of level-varying transition rules in bonus-malus systems onto risk-varying rules and combine both these ideas to formulate the generalization of varying transition rules. Moreover, we generalize the analytical formulae for the determination of optimal relativities under these rules. We find that the risk-varying transition rules are the most effective among the different specifications of transition rules. Our numerical results also indicate that the resulting optimal relativities under the general-varying rules are higher than those of under the risk-varying rules partly due to the differences of the transitions imposed by the rules.
Original languageEnglish
Pages (from-to)134-140
Number of pages7
JournalInsurance: Mathematics and Economics
Publication statusPublished - May 2016
Externally publishedYes


  • Bonus–malus system
  • Transition rules
  • Optimal relativities
  • a priori claim frequency
  • a posteriori rating

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