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

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  • Gareth W. Peters
  • Wilson Y. Chen
  • Richard H. Gerlach

Abstract

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class 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 parameterizations 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 with such models is to perform robust estimation for the loss model parameters that will be amenable to practitioners when fitting such models. In this paper we develop a novel, efficient and robust estimation procedure for estimation of model parameters in this family Tukey transform models, based on L-moments. It is shown to be more robust and efficient than current state of the art methods of estimation for such families of loss models and is simple to implement for practical purposes.

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  • Gareth W. Peters & Wilson Y. Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments," Papers 1603.01041, arXiv.org.
  • Handle: RePEc:arx:papers:1603.01041
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    File URL: http://arxiv.org/pdf/1603.01041
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    References listed on IDEAS

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    1. Cummins, J. David & Dionne, Georges & McDonald, James B. & Pritchett, B. Michael, 1990. "Applications of the GB2 family of distributions in modeling insurance loss processes," Insurance: Mathematics and Economics, Elsevier, vol. 9(4), pages 257-272, December.
    2. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Model uncertainty in claims reserving within Tweedie's compound Poisson models," Papers 0904.1483, arXiv.org.
    3. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    4. 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.
    5. Chan, Jennifer S.K. & Boris Choy, S.T. & Makov, Udi E., 2008. "Robust Bayesian Analysis of Loss Reserves Data Using the Generalized-t Distribution," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(01), pages 207-230, May.
    6. Kabir K. Dutta & David F. Babbel, 2002. "On Measuring Skewness and Kurtosis in Short Rate Distributions: The Case of the US Dollar London Inter Bank Offer Rates," Center for Financial Institutions Working Papers 02-25, Wharton School Center for Financial Institutions, University of Pennsylvania.
    7. Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(02), pages 265-291, November.
    8. 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.
    9. 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.
    10. Kabir Dutta & Jason Perry, 2006. "A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital," Working Papers 06-13, Federal Reserve Bank of Boston.
    11. Dong, A.X.D. & Chan, J.S.K., 2013. "Bayesian analysis of loss reserving using dynamic models with generalized beta distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 355-365.
    12. Matthias Fischer, 2010. "Generalized Tukey-type distributions with application to financial and teletraffic data," Statistical Papers, Springer, vol. 51(1), pages 41-56, January.
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    Cited by:

    1. 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.
    2. Wilson Ye Chen & Gareth W. Peters & Richard H. Gerlach & Scott A. Sisson, 2017. "Dynamic Quantile Function Models," Papers 1707.02587, arXiv.org, revised Sep 2017.
    3. Gareth Peters & Pavel Shevchenko & Bertrand 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.
    4. 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.

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