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Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments

Author

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  • Gareth W. Peters

    (Department of Statistical Science, University College London, London WC1E 6BT, UK
    Oxford-Man Institute, Oxford University, Oxford OX2 6ED, UK
    System Risk Center, London School of Economics, London WC2A 2AE, UK)

  • Wilson Ye Chen

    (Discipline of Business Analytics, The University of Sydney, Sydney 2006, Australia)

  • Richard H. Gerlach

    (Discipline of Business Analytics, The University of Sydney, Sydney 2006, Australia)

Abstract

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class of Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterisations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling. One of the challenges that are amenable to practitioners when fitting such models is to perform robust estimation of the model parameters. In this paper we develop a novel, efficient, and robust procedure for estimating the parameters of this family of Tukey transform models, based on L-moments. It is shown to be more efficient than the current state of the art estimation methods for such families of loss models while being simple to implement for practical purposes.

Suggested Citation

  • Gareth W. Peters & Wilson Ye Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments," Risks, MDPI, vol. 4(2), pages 1-41, May.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:2:p:14-:d:70470
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    References listed on IDEAS

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    5. Gareth W. Peters & Pavel Shevchenko & Mark Young & Wendy Yip, 2011. "Analytic Loss Distributional Approach Model for Operational Risk from the alpha-Stable Doubly Stochastic Compound Processes and Implications for Capital Allocation," Papers 1102.3582, arXiv.org.
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    11. Peters, Gareth W. & Shevchenko, Pavel V. & Young, Mark & Yip, Wendy, 2011. "Analytic loss distributional approach models for operational risk from the α-stable doubly stochastic compound processes and implications for capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 565-579.
    12. Xu, Yihuan & Iglewicz, Boris & Chervoneva, Inna, 2014. "Robust estimation of the parameters of g-and-h distributions, with applications to outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 66-80.
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    Citations

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    Cited by:

    1. Marco Bee & Julien Hambuckers & Luca Trapin, 2019. "An improved approach for estimating large losses in insurance analytics and operational risk using the g-and-h distribution," DEM Working Papers 2019/11, Department of Economics and Management.
    2. Gareth W. Peters & Pavel V. Shevchenko & Bertrand K. Hassani & Ariane Chapelle, 2016. "Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01391091, HAL.
    3. Marco Bee, 2022. "The truncated g-and-h distribution: estimation and application to loss modeling," Computational Statistics, Springer, vol. 37(4), pages 1771-1794, September.
    4. Gareth W. Peters & Pavel V. Shevchenko & Bertrand Hassani & Ariane Chapelle, 2016. "Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?," Papers 1607.02319, arXiv.org, revised Sep 2016.
    5. Marco Bee & Julien Hambuckers & Flavio Santi & Luca Trapin, 2021. "Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach," Computational Statistics, Springer, vol. 36(3), pages 2177-2200, September.
    6. Gareth W. Peters & Pavel V. Shevchenko & Bertrand K. Hassani & Ariane Chapelle, 2016. "Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?," Post-Print halshs-01391091, HAL.
    7. Holly Brannelly & Andrea Macrina & Gareth W. Peters, 2019. "Quantile Diffusions for Risk Analysis," Papers 1912.10866, arXiv.org, revised Sep 2021.
    8. Wilson Ye Chen & Gareth W. Peters & Richard H. Gerlach & Scott A. Sisson, 2017. "Dynamic Quantile Function Models," Papers 1707.02587, arXiv.org, revised May 2021.
    9. Gareth W. Peters, 2018. "General Quantile Time Series Regressions for Applications in Population Demographics," Risks, MDPI, vol. 6(3), pages 1-47, September.
    10. Gareth W. Peters & Pavel V. Shevchenko & Bertrand K. Hassani & Ariane Chapelle, 2016. "Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?," Documents de travail du Centre d'Economie de la Sorbonne 16065, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    11. Holly Brannelly & Andrea Macrina & Gareth W. Peters, 2021. "Stochastic measure distortions induced by quantile processes for risk quantification and valuation," Papers 2201.02045, arXiv.org.

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