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Designing Optimal Bonus-Malus Systems from Different Types of Claims

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  • Pinquet, J.

Abstract

This paper provides bonus-malus systems which rest on different types of claims. Consistent estimators are given for some moments of themixing distribution of a multi equation Poisson model with random effects. Bonus-malus coefficients are then obtained with the expected value principle, and from linear credibility predictors. E,pirical results are presented for two types of claims, namely claims with or without liability with respect to a third party.

Suggested Citation

  • Pinquet, J., 1998. "Designing Optimal Bonus-Malus Systems from Different Types of Claims," Papers 9819, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  • Handle: RePEc:fth:pnegmi:9819
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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: The Journal of the International Actuarial Association, Cambridge University Press, vol. 19(02), pages 199-212, November.
    2. J. Pinquet., 1997. "Testing heterogenity through consistent estimators," THEMA Working Papers 97-14, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. Dionne, G. & Maurice, M. & Pinquet, J. & Vanasse, C., 2001. "The Role of Memory in Long-Term Contracting with Moral Hazard: Empirical Evidence in Automobile Insurance," Ecole des Hautes Etudes Commerciales de Montreal- 01-05, Ecole des Hautes Etudes Commerciales de Montreal-Chaire de gestion des risques..
    4. J. Pinquet, 1997. "Experience rating through heterogeneous models," THEMA Working Papers 97-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. Bühlmann, Hans, 1967. "Experience Rating and Credibility," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 4(03), pages 199-207, July.
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    Cited by:

    1. Desjardins, Denise & Dionne, Georges & Pinquet, Jean, 2001. "Experience Rating Schemes for Fleets of Vehicles," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 31(01), pages 81-105, May.
    2. Asamoah, Kwadwo, 2016. "On the credibility of insurance claim frequency: Generalized count models and parametric estimators," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 339-353.
    3. Katrien Antonio & Emiliano Valdez, 2012. "Statistical concepts of a priori and a posteriori risk classification in insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 187-224, June.
    4. DENUIT, Michel & SAILLET, Olivier, 2001. "Nonparametric Tests for Positive Quadrant Dependence," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 01 Apr 2001.
    5. Angers, Jean-François & Desjardins, Denise & Dionne, Georges, 2004. "Modèle Bayésien de tarification de l’assurance des flottes de véhicules," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 253-303, Juin-Sept.
    6. Young, Gary & Valdez, Emiliano A. & Kohn, Robert, 2009. "Multivariate probit models for conditional claim-types," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 214-228, April.
    7. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2016. "Sarmanov family of multivariate distributions for bivariate dynamic claim counts model," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 120-133.
    8. Shi, Peng & Valdez, Emiliano A., 2011. "A copula approach to test asymmetric information with applications to predictive modeling," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 226-239, September.
    9. Satya P. DAS & Chetan CHATE, 2001. "Endogenous Distribution, Politics, and Growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001019, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    10. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2006. "Vehicle and Fleet Random Effects in a Model of Insurance Rating for Fleets of Vehicles," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(01), pages 25-77, May.
    11. Natacha Brouhns & Montserrat Guillén & Michel Denuit & Jean Pinquet, 2003. "Bonus-Malus Scales in Segmented Tariffs With Stochastic Migration Between Segments," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 577-599.
    12. Olena Ragulina, 2017. "Bonus--malus systems with different claim types and varying deductibles," Papers 1707.00917, arXiv.org.
    13. Jean Pinquet, 2012. "Experience rating in non-life insurance," Working Papers hal-00677100, HAL.
    14. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.

    More about this item

    Keywords

    INSURANCE;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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