Double-counting problem of the bonus–malus system

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

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1 Scopus citations


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

Bibliographical note

Funding Information:
Rosy Oh was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), Republic of Korea funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177 ). Sojung C. Park acknowledges support from the Institute of Management Research at Seoul National University, Republic of Korea and the Institute of Finance and Banking at Seoul National University, Republic of Korea . Jae Youn Ahn was supported by a National Research Foundation of Korea (NRF), Republic of Korea grant funded by the Korean Government (NRF-2017R1D1A1B03032318 ). We also appreciate the valuable comments, which helped us to revise the paper, by anonymous referees and the editor during the revision process.

Publisher Copyright:
© 2020 Elsevier B.V.


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


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