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Bayesian credibility for GLMs

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  • Xacur, Oscar Alberto Quijano
  • Garrido, José

Abstract

We revisit the classical credibility results of Jewell (1974) and Bühlmann (1967) to obtain credibility premiums for a GLM using a modern Bayesian approach. Here the prior distribution can be chosen without restrictions to be conjugate to the response distribution. It can even come from out-of-sample information if the actuary prefers.

Suggested Citation

  • Xacur, Oscar Alberto Quijano & Garrido, José, 2018. "Bayesian credibility for GLMs," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 180-189.
    • Handle: RePEc:eee:insuma:v:83:y:2018:i:c:p:180-189
    DOI: 10.1016/j.insmatheco.2018.05.001
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    References listed on IDEAS

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    1. Nelder, J.A. & Verrall, R.J., 1997. "Credibility Theory and Generalized Linear Models," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 71-82, May.
    2. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    3. De Vylder, F., 1985. "Non-linear regression in credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 163-172, July.
    4. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, September.
    5. José Bernardo, 2005. "Intrinsic credible regions: An objective Bayesian approach to interval estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 317-384, December.
    6. Jewell, William S., 1974. "Credible Means are exact Bayesian for Exponential Families," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 77-90, September.
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    Cited by:

    1. Sebastian Calcetero-Vanegas & Andrei L. Badescu & X. Sheldon Lin, 2022. "Effective a Posteriori Ratemaking with Large Insurance Portfolios via Surrogate Modeling," Papers 2211.06568, arXiv.org, revised May 2023.
    2. Chen, Yongzhao & Cheung, Ka Chun & Choi, Hugo Ming Cheung & Yam, Sheung Chi Phillip, 2020. "Evolutionary credibility risk premium," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 216-229.

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