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A Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums

Author

Listed:
  • Emilio Gómez-Déniz

    (Department of Quantitative Methods and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain)

  • Enrique Calderín-Ojeda

    (Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Melbourne, VIC 3010, Australia)

Abstract

In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and below a given claim size threshold in an automobile insurance portfolio. Relevant properties of this model are given. Next, a mixed regression model is derived to compute credibility bonus-malus premiums based on the individual claim size and other risk factors such as gender, type of vehicle, driving area, or age of the vehicle. Results are illustrated by using a well-known automobile insurance portfolio dataset.

Suggested Citation

  • Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2020. "A Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums," Risks, MDPI, vol. 8(1), pages 1-19, February.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:1:p:20-:d:323719
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    References listed on IDEAS

    as
    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
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    3. Pinquet, Jean, 1998. "Designing Optimal Bonus-Malus Systems from Different Types of Claims," ASTIN Bulletin, Cambridge University Press, vol. 28(2), pages 205-220, November.
    4. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, October.
    5. Vernic, Raluca, 1997. "On The Bivariate Generalized Poisson Distribution," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 23-32, May.
    6. Walhin, J.F. & Paris, J., 2001. "The Mixed Bivariate Hofmann Distribution," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 123-138, May.
    7. Partrat, Christian, 1994. "Compound model for two dependent kinds of claim," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 219-231, December.
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    9. Walhin, J.F. & Paris, J., 2000. "Recursive Formulae for Some Bivariate Counting Distributions Obtained by the Trivariate Reduction Method," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 141-155, May.
    10. 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.
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