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Bonus-Malus premiums under the dependent frequency-severity modeling

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  • Rosy Oh
  • Peng Shi
  • Jae Youn Ahn

Abstract

A Bonus-Malus System (BMS) in insurance is a premium adjustment mechanism widely used in a posteriori ratemaking process to set the premium for the next contract period based on a policyholder's claim history. The current practice in BMS implementation relies on the assumption of independence between claim frequency and severity, despite the fact that a series of recent studies report evidence of a significant frequency-severity relationship, particularly in automobile insurance. To address this discrepancy, we propose a copula-based correlated random effects model to accommodate the dependence between claim frequency and severity, and further illustrate how to incorporate such dependence into the current BMS. We derive analytical solutions to the optimal relativities under the proposed framework and provide numerical experiments based on real data analysis to assess the effect of frequency-severity dependence in BMS ratemaking.

Suggested Citation

  • Rosy Oh & Peng Shi & Jae Youn Ahn, 2020. "Bonus-Malus premiums under the dependent frequency-severity modeling," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(3), pages 172-195, March.
  • Handle: RePEc:taf:sactxx:v:2020:y:2020:i:3:p:172-195
    DOI: 10.1080/03461238.2019.1655477
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    Cited by:

    1. Shi, Peng & Zhao, Zifeng, 2024. "Enhanced pricing and management of bundled insurance risks with dependence-aware prediction using pair copula construction," Journal of Econometrics, Elsevier, vol. 240(1).
    2. Li, Yinhuan & Fung, Tsz Chai & Peng, Liang & Qian, Linyi, 2023. "Diagnostic tests before modeling longitudinal actuarial data," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 310-325.

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