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Claims reserving in the hierarchical generalized linear model framework

Author

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  • Gigante, Patrizia
  • Picech, Liviana
  • Sigalotti, Luciano

Abstract

We consider an approach based on the hierarchical generalized linear models and h-likelihood estimators for claims reserving in non-life insurance. The hierarchical generalized linear models represent a class of flexible mixture models that extend the generalized linear models and the generalized linear mixed models. The fitting algorithm and the inferential analyses can be obtained by applying standard procedures to one or more generalized linear models, suitably defined. Our study examines how the models can be used to obtain predictors of the claims reserves and to determine their prediction uncertainty.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:381-390
    DOI: 10.1016/j.insmatheco.2013.02.006
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    References listed on IDEAS

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    1. England, P. D. & Verrall, R. J., 2006. "Predictive Distributions of Outstanding Liabilities in General Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 221-270, September.
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    9. England, Peter D. & Verrall, Richard J. & Wüthrich, Mario V., 2012. "Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method," Annals of Actuarial Science, Cambridge University Press, vol. 6(2), pages 258-283, September.
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    12. Verrall, R.J. & England, P.D., 2005. "Incorporating expert opinion into a stochastic model for the chain-ladder technique," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 355-370, October.
    13. Alai, D. H. & Merz, M. & Wüthrich, M. V., 2009. "Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method," Annals of Actuarial Science, Cambridge University Press, vol. 4(1), pages 7-31, March.
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    Cited by:

    1. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    2. Benjamin Avanzi & Gregory Clive Taylor & Phuong Anh Vu & Bernard Wong, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Papers 2004.06880, arXiv.org.

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    More about this item

    Keywords

    Claims reserving; Conditional mean square error of prediction; Hierarchical generalized linear models; h-likelihood; Quasi-hierarchical generalized linear models;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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