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A Robust General Multivariate Chain Ladder Method

Author

Listed:
  • Kris Peremans

    (Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
    These authors contributed equally to this work.)

  • Stefan Van Aelst

    (Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
    These authors contributed equally to this work.)

  • Tim Verdonck

    (Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
    These authors contributed equally to this work.)

Abstract

The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) do not need to be equal to the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue, we propose a robust alternative that estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to automatically flag the claims with a significantly large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data.

Suggested Citation

  • Kris Peremans & Stefan Van Aelst & Tim Verdonck, 2018. "A Robust General Multivariate Chain Ladder Method," Risks, MDPI, vol. 6(4), pages 1-18, September.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:4:p:108-:d:172919
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    References listed on IDEAS

    as
    1. Peremans, Kris & Van Aelst, Stefan, 2018. "Robust inference for seemingly unrelated regression models," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 212-224.
    2. 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.
    3. 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.
    4. Ajne, Björn, 1994. "Additivity of Chain-Ladder Projections," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 311-318, November.
    5. Zhang, Yanwei, 2010. "A general multivariate chain ladder model," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 588-599, June.
    6. 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.
    7. Michael Merz & Mario Wüthrich, 2008. "Prediction Error of the Multivariate Chain Ladder Reserving Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 175-197.
    8. Verdonck, T. & Van Wouwe, M., 2011. "Detection and correction of outliers in the bivariate chain-ladder method," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 188-193, September.
    9. Braun, Christian, 2004. "The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 399-423, November.
    10. Vytaras Brazauskas, 2009. "Robust and Efficient Fitting of Loss Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 356-369.
    11. Merz, M. & Wüthrich, M. V., 2007. "Prediction Error of the Chain Ladder Reserving Method applied to Correlated Run-off Triangles," Annals of Actuarial Science, Cambridge University Press, vol. 2(1), pages 25-50, March.
    12. 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.
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    Cited by:

    1. Ioannis Badounas & Georgios Pitselis, 2020. "Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model," Risks, MDPI, vol. 8(1), pages 1-26, February.
    2. Kevin Kuo, 2019. "DeepTriangle: A Deep Learning Approach to Loss Reserving," Risks, MDPI, vol. 7(3), pages 1-12, September.

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