Bonus-Malus premiums under the dependent frequency-severity modeling

Rosy Oh, Peng Shi, Jae Youn Ahn

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17 Scopus citations


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.

Original languageEnglish
Pages (from-to)172-195
Number of pages24
JournalScandinavian Actuarial Journal
Issue number3
StatePublished - 15 Mar 2020

Bibliographical note

Funding Information:
Jae Youn Ahn was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (NRF-2017R1D1A1B03032318).

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • bivariate random effects
  • bonus-malus system
  • copula
  • Frequency-severity dependence


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