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On the impact of outliers in loss reserving

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  • Benjamin Avanzi
  • Mark Lavender
  • Greg Taylor
  • Bernard Wong

Abstract

The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a consequence the chain-ladder reserving technique is non-robust. In this paper we investigate the sensitivity of reserves and mean squared errors of prediction under Mack's Model (Mack, 1993). This is done through the derivation of impact functions which are calculated by taking the first derivative of the relevant statistic of interest with respect to an observation. We also provide and discuss the impact functions for quantiles when total reserves are assumed to be lognormally distributed. Additionally, comparisons are made between the impact functions for individual accident year reserves under Mack's Model and the Bornhuetter-Ferguson methodology. It is shown that the impact of incremental claims on these statistics of interest varies widely throughout a loss triangle and is heavily dependent on other cells in the triangle. Results are illustrated using data from a Belgian non-life insurer.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2203.00184
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. 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.
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    Cited by:

    1. 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.
    2. Greg Taylor & Gráinne McGuire, 2023. "Model Error (or Ambiguity) and Its Estimation, with Particular Application to Loss Reserving," Risks, MDPI, vol. 11(11), pages 1-28, October.
    3. 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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