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Adjusting the Premium Relativities in a Bonus-Malus System: An Integrated Approach Using the First Claim Time and the Number of Claims

Author

Listed:
  • Mahmoudvand Rahim

    (Department of Statistics, Bu-Ali Sina University, Hamedan, Iran)

  • Tan Chong It

    (Department of Applied Finance and Actuarial Studies, Macquarie University, New South Wales, Australia)

  • Abbasi Narges

    (Department of Statistics, Payame Noor University, I. R.Iran)

Abstract

In this paper, we propose an integrated approach to adjust the premium relativities in a bonus-malus system by using the information of the first claim time (expressed in terms of sub-period in a year) and the number of claims reported by individual policyholder. We provide a formal representation for the newly proposed structure and derive the analytical expressions for the adjusted premium relativities. Other things being equal, a lower adjusted premium relativity is imposed for an earlier sub-period of the first claim made, whereas policyholders with more claims are subject to a higher adjusted premium relativity.

Suggested Citation

  • Mahmoudvand Rahim & Tan Chong It & Abbasi Narges, 2017. "Adjusting the Premium Relativities in a Bonus-Malus System: An Integrated Approach Using the First Claim Time and the Number of Claims," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 11(2), pages 1-19, July.
    • Handle: RePEc:bpj:apjrin:v:11:y:2017:i:2:p:19:n:3
    DOI: 10.1515/apjri-2016-0038
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    References listed on IDEAS

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    1. Frangos, Nicholas E. & Vrontos, Spyridon D., 2001. "Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 1-22, May.
    2. Mahmoudvand, Rahim & Hassani, Hossein, 2009. "Generalized Bonus-Malus Systems with a Frequency and a Severity Component on an Individual Basis in Automobile Insurance," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 307-315, May.
    3. de Lourdes Centeno, Maria & Manuel Andrade e Silva, Joao, 2001. "Bonus systems in an open portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 341-350, June.
    4. repec:cup:astinb:v:19:y:1989:i:02:p:199-212_00 is not listed on IDEAS
    5. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
    6. Søren Asmussen, 2014. "Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction," Risks, MDPI, vol. 2(1), pages 1-25, March.
    7. Pitrebois, Sandra & Denuit, Michel & Walhin, Jean-François, 2003. "Setting a Bonus-Malus Scale in the Presence of Other Rating Factors: Taylor's Work Revisited," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 419-436, November.
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    Cited by:

    1. Okura Mahito & Yoshizawa Takuya & Sakaki Motohiro, 2021. "An Evaluation of the New Japanese Bonus–Malus System with No-claim and Claimed Subclasses," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 15(1), pages 1-12, January.

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