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Bivariate credibility bonus–malus premiums distinguishing between two types of claims

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  • Gómez-Déniz, E.

Abstract

We propose a modification of the bonus–malus system of tarification that is commonly applied in automobile insurance. Under the standard system, the premium assigned to each policyholder is based only on the number of claims made. Therefore, a policyholder who has had an accident producing a relatively small amount of loss is penalised to the same extent as one who has had a more costly accident. This outcome would seem to be unfair.

Suggested Citation

  • Gómez-Déniz, E., 2016. "Bivariate credibility bonus–malus premiums distinguishing between two types of claims," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 117-124.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:117-124
    DOI: 10.1016/j.insmatheco.2016.06.009
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    References listed on IDEAS

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    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.
    2. Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
    3. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, November.
    4. Sarabia, José María & Gómez-Déniz, Emilio & Vázquez-Polo, Francisco J., 2004. "On the Use of Conditional Specification Models in Claim Count Distributions: an Application to Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 85-98, May.
    5. 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.
    6. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
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    Cited by:

    1. Simon, Pierre-Alexandre & Trufin, Julien & Denuit, Michel, 2023. "Bivariate Poisson credibility model and bonus-malus scale for claim and near-claim events," LIDAM Discussion Papers ISBA 2023014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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