Optimal relativities and transition rules of a bonus-malus system

Chong It Tan*, Jackie Li, Johnny Siu Hang Li, Uditha Balasooriya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


When a bonus-malus system with a single set of optimal relativities and a set of simple transition rules is implemented, two inadequacy scenarios are induced because all policyholders are subject to the same a posteriori premium relativities (level transitions) independent of their a priori characteristics (current levels occupied). In this paper we propose a new objective function in the determination of optimal relativities that directly incorporates the a priori expected claim frequencies to partially address one of the inadequacy scenarios. We derive the analytical solution for the optimal relativities under a financial equilibrium constraint. Furthermore, we introduce a metric called effectiveness of transition rules to compare the different specifications of transition rules. We also argue that varying transition rules which are more flexible in addressing the other inadequacy scenario may be more effective than their corresponding simple rules.

Original languageEnglish
Pages (from-to)255-263
Number of pages9
JournalInsurance: Mathematics and Economics
Publication statusPublished - 1 Mar 2015
Externally publishedYes


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