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Double-counting problem of the bonus–malus system

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

Insurance: Mathematics and Economics, 2020, vol. 93, issue C, 141-155

Abstract: 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.

Keywords: Bonus–malus system; Ratemaking; Double counting; Optimization; Auto insurance (search for similar items in EconPapers)
JEL-codes: C30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.insmatheco.2020.04.008

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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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