Double-counting problem of the bonus–malus system

Rosy Oh, Kyung Suk Lee, Sojung C. Park, Jae Youn Ahn

Research output: Contribution to journalArticlepeer-review


The bonus–malus system (BMS) is a widely used premium adjustment mechanism based on policyholder's claim history. Most auto insurance BMSs assume that policyholders in the same bonus–malus (BM) level share the same a posteriori risk adjustment. This system reflects the policyholder's claim history in a relatively simple manner. However, the typical system follows a single BM scale and is known to suffer from the double-counting problem: policyholders in the high-risk classes in terms of a priori characteristics are penalized too severely (Taylor, 1997; Pitrebois et al., 2003). Thus, Pitrebois et al. (2003) proposed a new system with multiple BM scales based on the a priori characteristics. While this multiple-scale BMS removes the double-counting problem, it loses the prime benefit of simplicity. Alternatively, we argue that the double-counting problem can be viewed as an inefficiency of the optimization process. Furthermore, we show that the double-counting problem can be resolved by fully optimizing the BMS setting, but retaining the traditional BMS format.

Original languageEnglish
Pages (from-to)141-155
Number of pages15
JournalInsurance: Mathematics and Economics
StatePublished - Jul 2020


  • Auto insurance
  • Bonus–malus system
  • Double counting
  • Optimization
  • Ratemaking


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