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Robust Estimation of Reserve Risk

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  • Busse, Marc
  • Müller, Ulrich
  • Dacorogna, Michel

Abstract

We tackle problems that appear in the practical application of the Mack method for the estimation of reserving risk and the bootstrapping of ultimate reserve distributions. More specifically, we design a filter for outliers and large jumps, and present a robust version of Mack's variance estimator. A combination of these guarantees a reasonable Mack and bootstrap error even for deficient data. Furthermore, a method is derived that allows us to remove the influence of fluctuations in earning patterns from the reserve risk estimate. It is thereby shown that the relation between underwriting and accident year based loss development patterns is given by a convolution. A numerically stable inversion thereof is obtained by means of a Tikhonov regularization. The reliability of the presented methods is verified with several loss triangles.

Suggested Citation

  • Busse, Marc & Müller, Ulrich & Dacorogna, Michel, 2010. "Robust Estimation of Reserve Risk," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 453-489, November.
    • Handle: RePEc:cup:astinb:v:40:y:2010:i:02:p:453-489_00
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    Cited by:

    1. Michel Dacorogna & Alessandro Ferriero & David Krief, 2018. "One-Year Change Methodologies for Fixed-Sum Insurance Contracts," Risks, MDPI, vol. 6(3), pages 1-29, July.
    2. Michel Dacorogna, 2023. "How to Gain Confidence in the Results of Internal Risk Models? Approaches and Techniques for Validation," Risks, MDPI, vol. 11(5), pages 1-20, May.
    3. Dacorogna, Michel M, 2017. "Approaches and Techniques to Validate Internal Model Results," MPRA Paper 79632, University Library of Munich, Germany.
    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. Rüdiger Kiesel & Robin Rühlicke & Gerhard Stahl & Jinsong Zheng, 2016. "The Wasserstein Metric and Robustness in Risk Management," Risks, MDPI, vol. 4(3), pages 1-14, August.

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