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Bayes and Empirical Bayes Estimation for the Chain Ladder Model

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  • Verrall, R.J.

Abstract

The subject of predicting outstanding claims on a porfolio of general insurance policies is approached via the theory of hierarchical Bayesian linear models. This is particularly appropriate since the chain ladder technique can be expressed in the form of a linear model. The statistical methods which are applied allow the practitioner to use different modelling assumptions from those implied by a classical formulation, and to arrive at forecasts which have a greater degree of inherent stability. The results can also be used for other linear models. By using a statistical structure, a sound approach to the chain ladder technique can be derived. The Bayesian results allow the input of collateral information in a formal manner. Empirical Bayes results are derived which can be interpreted as credibility estimates. The statistical assumptions which are made in the modelling procedure are clearly set out and can be tested by the practitioner. The results based on the statistical theory form one part of the reserving procedure, and should be followed by expert interpretation and analysis. An illustration of the use of Bayesian and empirical Bayes estimation methods is given.

Suggested Citation

  • Verrall, R.J., 1990. "Bayes and Empirical Bayes Estimation for the Chain Ladder Model," ASTIN Bulletin, Cambridge University Press, vol. 20(2), pages 217-243, November.
    • Handle: RePEc:cup:astinb:v:20:y:1990:i:02:p:217-243_00
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    Cited by:

    1. Boratyńska, Agata, 2017. "Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 135-140.
    2. Bente Corneliu Cristian & Gavriletea Marius Dan, 2015. "Inflation Adjusted Chain Ladder Method," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 370-379, December.
    3. Peng Shi, 2017. "A Multivariate Analysis of Intercompany Loss Triangles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 717-737, June.
    4. Corneliu Cristian Bente, 2017. "Actuarial Estimation Of Technical Reserves In Insurance Companies. Basic Chain Ladder Method," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 227-234, July.
    5. Andreas Frohlich & Annegret Weng, 2016. "Parameter uncertainty and reserve risk under Solvency II," Papers 1612.03066, arXiv.org, revised Apr 2017.
    6. Verrall, Richard, 1996. "Claims reserving and generalised additive models," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 31-43, December.
    7. Corneliu Cristian Bente, 2017. "Inflation Adjusted Chain Ladder Method As A Challenge To Actuaries," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 157-165, December.

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