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Full Bayesian analysis of claims reserving uncertainty

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  • Peters, Gareth W.
  • Targino, Rodrigo S.
  • Wüthrich, Mario V.

Abstract

We revisit the gamma–gamma Bayesian chain-ladder (BCL) model for claims reserving in non-life insurance. This claims reserving model is usually used in an empirical Bayesian way using plug-in estimates for the variance parameters. The advantage of this empirical Bayesian framework is that allows us for closed form solutions. The main purpose of this paper is to develop the full Bayesian case also considering prior distributions for the variance parameters and to study the resulting sensitivities.

Suggested Citation

  • Peters, Gareth W. & Targino, Rodrigo S. & Wüthrich, Mario V., 2017. "Full Bayesian analysis of claims reserving uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 41-53.
    • Handle: RePEc:eee:insuma:v:73:y:2017:i:c:p:41-53
    DOI: 10.1016/j.insmatheco.2016.12.007
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    References listed on IDEAS

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    1. Gisler, Alois & Wüthrich, Mario V., 2008. "Credibility for the Chain Ladder Reserving Method," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 565-600, November.
    2. Gisler, Alois, 2006. "The Estimation Error in the Chain-Ladder Reserving Method: A Bayesian Approach," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 554-565, November.
    3. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    4. Renshaw, A.E. & Verrall, R.J., 1998. "A Stochastic Model Underlying the Chain-Ladder Technique," British Actuarial Journal, Cambridge University Press, vol. 4(4), pages 903-923, October.
    5. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    6. Mario V. Wuthrich & Michael Merz, 2015. "Stochastic Claims Reserving Manual: Advances in Dynamic Modeling," Swiss Finance Institute Research Paper Series 15-34, Swiss Finance Institute.
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    Citations

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    Cited by:

    1. Carnevale Giulio Ercole & Clemente Gian Paolo, 2020. "A Bayesian Internal Model for Reserve Risk: An Extension of the Correlated Chain Ladder," Risks, MDPI, vol. 8(4), pages 1-20, November.
    2. Fröhlich, Andreas & Weng, Annegret, 2018. "Parameter uncertainty and reserve risk under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 130-141.
    3. Gareth W. Peters & Rodrigo S. Targino & Mario V. Wüthrich, 2017. "Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks," Risks, MDPI, vol. 5(4), pages 1-51, September.
    4. Andreas Frohlich & Annegret Weng, 2016. "Parameter uncertainty and reserve risk under Solvency II," Papers 1612.03066, arXiv.org, revised Apr 2017.
    5. Gao, Guangyuan & Meng, Shengwang & Shi, Yanlin, 2021. "Dispersion modelling of outstanding claims with double Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 572-586.

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