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On the Use of Conditional Specification Models in Claim Count Distributions: an Application to Bonus-Malus Systems

Author

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  • Sarabia, José María
  • Gómez-Déniz, Emilio
  • Vázquez-Polo, Francisco J.

Abstract

In this paper a new methodology using the conditional specification technique intoduced by Arnold et al. (1999) is used to obtain bonus-malus premiums. A Poisson distribution for which the parameter is a function of the classical structure parameter is used and a new class of prior distribution arises in a natural way. This model contains, as a particular case, the classical compound Poisson model and is found to be much more robust than earlier ones. An example is given to illustrate our ideas.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:34:y:2004:i:01:p:85-98_01
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    Citations

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    Cited by:

    1. Sarabia, José María & Guillén, Montserrat, 2008. "Joint modelling of the total amount and the number of claims by conditionals," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 466-473, December.
    2. Arnold, Barry C. & Sarabia, José María, 2022. "Conditional specification of statistical models: Classical models, new developments and challenges," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2020. "Modeling the Conditional Dependence between Discrete and Continuous Random Variables with Applications in Insurance," Mathematics, MDPI, vol. 9(1), pages 1-15, December.
    4. 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.
    5. Azaare Jacob & Zhao Wu, 2020. "An Alternative Pricing System through Bayesian Estimates and Method of Moments in a Bonus-Malus Framework for the Ghanaian Auto Insurance Market," JRFM, MDPI, vol. 13(7), pages 1-15, July.
    6. Jacob Azaare & Zhao Wu & Bright Nana Kwame Ahia, 2022. "Exploring the Effects of Classical Auto Insurance Rating Variables on Premium in ARDL: Is the high Policyholders’ Premium in Ghana Justified?," SAGE Open, , vol. 12(4), pages 21582440221, October.
    7. Emilio Déniz & José Sarabia & F. Vázquez Polo, 2009. "Robust Bayesian bonus-malus premiums under the conditional specification model," Statistical Papers, Springer, vol. 50(3), pages 465-480, June.
    8. Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2018. "Multivariate Credibility in Bonus-Malus Systems Distinguishing between Different Types of Claims," Risks, MDPI, vol. 6(2), pages 1-11, April.

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