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Double-counting problem of the bonus–malus system

Author

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

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.

Suggested Citation

  • Oh, Rosy & Lee, Kyung Suk & Park, Sojung C. & Ahn, Jae Youn, 2020. "Double-counting problem of the bonus–malus system," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 141-155.
    • Handle: RePEc:eee:insuma:v:93:y:2020:i:c:p:141-155
    DOI: 10.1016/j.insmatheco.2020.04.008
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    References listed on IDEAS

    as
    1. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    2. Taylor, Greg, 1997. "Setting a Bonus-Malus Scale in the Presence of other Rating Factors," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 319-327, November.
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    5. Tan, Chong It & Li, Jackie & Li, Johnny Siu-Hang & Balasooriya, Uditha, 2015. "Optimal relativities and transition rules of a bonus–malus system," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 255-263.
    6. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
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    More about this item

    Keywords

    Bonus–malus system; Ratemaking; Double counting; Optimization; Auto insurance;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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