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The influence of individual claims on the chain-ladder estimates: Analysis and diagnostic tool

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  • Verdonck, T.
  • Debruyne, M.

Abstract

The chain-ladder method is a widely used technique to forecast the reserves that have to be kept regarding claims that are known to exist, but for which the actual size is unknown at the time the reserves have to be set. In practice it can be easily seen that even one outlier can lead to a huge over- or underestimation of the overall reserve when using the chain-ladder method. This indicates that individual claims can be very influential when determining the chain-ladder estimates. In this paper the effect of contamination is mathematically analyzed by calculating influence functions in the generalized linear model framework corresponding to the chain-ladder method. It is proven that the influence functions are unbounded, confirming the sensitivity of the chain-ladder method to outliers. A robust alternative is introduced to estimate the generalized linear model parameters in a more outlier resistant way. Finally, based on the influence functions and the robust estimators, a diagnostic tool is presented highlighting the influence of every individual claim on the classical chain-ladder estimates. With this tool it is possible to detect immediately which claims have an abnormally positive or negative influence on the reserve estimates. Further examination of these influential points is then advisable. A study of artificial and real run-off triangles shows the good performance of the robust chain-ladder method and the diagnostic tool.

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  • Verdonck, T. & Debruyne, M., 2011. "The influence of individual claims on the chain-ladder estimates: Analysis and diagnostic tool," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 85-98, January.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:85-98
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    References listed on IDEAS

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    1. Verrall, R. J., 1991. "On the estimation of reserves from loglinear models," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 75-80, March.
    2. Verbeek, H. G., 1972. "An approach to the analysis of claims experience in motor liability excess of loss reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 6(3), pages 195-202, May.
    3. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    4. 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.
    5. England, Peter & Verrall, Richard, 1999. "Analytic and bootstrap estimates of prediction errors in claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 281-293, December.
    6. 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.
    7. 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.
    8. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    9. 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.
    10. Paulo J. R. Pinheiro & João Manuel Andrade e Silva & Maria De Lourdes Centeno, 2003. "Bootstrap Methodology in Claim Reserving," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 701-714, December.
    11. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
    12. Tim Verdonck & Martine Van Wouwe & Jan Dhaene, 2009. "A Robustification of the Chain-Ladder Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 280-298.
    13. Verrall, R. J., 2000. "An investigation into stochastic claims reserving models and the chain-ladder technique," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 91-99, February.
    14. John S. Preisser & Bahjat F. Qaqish, 1999. "Robust Regression for Clustered Data with Application to Binary Responses," Biometrics, The International Biometric Society, vol. 55(2), pages 574-579, June.
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    Cited by:

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    3. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.
    4. Pitselis, Georgios & Grigoriadou, Vasiliki & Badounas, Ioannis, 2015. "Robust loss reserving in a log-linear model," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 14-27.
    5. Benjamin Avanzi & Mark Lavender & Greg Taylor & Bernard Wong, 2022. "On the impact of outliers in loss reserving," Papers 2203.00184, arXiv.org, revised Jun 2023.
    6. Emmanuel Jordy Menvouta & Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2022. "mCube: Multinomial Micro-level reserving Model," Papers 2212.00101, arXiv.org.
    7. Steinmetz, Julia & Jentsch, Carsten, 2024. "Bootstrap consistency for the Mack bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 83-121.
    8. Jan Barlak & Matus Bakon & Martin Rovnak & Martina Mokrisova, 2022. "Heat Equation as a Tool for Outliers Mitigation in Run-Off Triangles for Valuing the Technical Provisions in Non-Life Insurance Business," Risks, MDPI, vol. 10(9), pages 1-17, August.
    9. Benjamin Avanzi & Mark Lavender & Greg Taylor & Bernard Wong, 2022. "Detection and treatment of outliers for multivariate robust loss reserving," Papers 2203.03874, arXiv.org, revised Jun 2023.

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