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Credibility Theory and Generalized Linear Models

Author

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  • Nelder, J.A.
  • Verrall, R.J.

Abstract

This paper shows how credibility theory can be encompassed within the theory of Hierarchical Generalized Linear Models. It is shown that credibility estimates are obtained by including random effects in the model. The framework of Hierarchical Generalized Linear Models allows a more extensive range of models to be used than straightforward credibility theory. The model fitting and testing procedures can be carried out using a standard statistical package. Thus, the paper contributes a further range of models which may be useful in a wide range of actuarial applications, including premium rating and claims reserving.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:27:y:1997:i:01:p:71-82_01
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    Citations

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    Cited by:

    1. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    2. Gigante, Patrizia & Picech, Liviana & Sigalotti, Luciano, 2013. "Claims reserving in the hierarchical generalized linear model framework," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 381-390.
    3. Landsman, Zinoviy, 2002. "Credibility theory: a new view from the theory of second order optimal statistics," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 351-362, June.
    4. Frees, Edward W. & Young, Virginia R. & Luo, Yu, 1999. "A longitudinal data analysis interpretation of credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 229-247, May.
    5. Lo, Chi Ho & Fung, Wing Kam & Zhu, Zhong Yi, 2006. "Generalized estimating equations for variance and covariance parameters in regression credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 99-113, August.
    6. Alicja Wolny-Dominiak & Tomasz Żądło, 2021. "The Measures of Accuracy of Claim Frequency Credibility Predictor," Sustainability, MDPI, vol. 13(21), pages 1-13, October.
    7. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    8. Xacur, Oscar Alberto Quijano & Garrido, José, 2018. "Bayesian credibility for GLMs," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 180-189.
    9. Marina Maniati & Evangelos Sambracos, 2017. "Decision-making process in shipping finance: A stochastic approach," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1317083-131, January.
    10. Yikai (Maxwell) Gong & Zhuangdi Li & Maria Milazzo & Kristen Moore & Matthew Provencher, 2018. "Credibility Methods for Individual Life Insurance," Risks, MDPI, vol. 6(4), pages 1-16, December.
    11. Paulsen, Jostein & Lunde, Astrid & Skaug, Hans Julius, 2008. "Fitting mixed-effects models when data are left truncated," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 121-133, August.
    12. Dornheim, Harald & Brazauskas, Vytaras, 2011. "Robust-efficient credibility models with heavy-tailed claims: A mixed linear models perspective," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 72-84, January.

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