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Pareto models for risk management

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  • Arthur Charpentier
  • Emmanuel Flachaire

Abstract

The Pareto model is very popular in risk management, since simple analytical formulas can be derived for financial downside risk measures (Value-at-Risk, Expected Shortfall) or reinsurance premiums and related quantities (Large Claim Index, Return Period). Nevertheless, in practice, distributions are (strictly) Pareto only in the tails, above (possible very) large threshold. Therefore, it could be interesting to take into account second order behavior to provide a better fit. In this article, we present how to go from a strict Pareto model to Pareto-type distributions. We discuss inference, and derive formulas for various measures and indices, and finally provide applications on insurance losses and financial risks.

Suggested Citation

  • Arthur Charpentier & Emmanuel Flachaire, 2019. "Pareto models for risk management," Papers 1912.11736, arXiv.org.
    • Handle: RePEc:arx:papers:1912.11736
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    References listed on IDEAS

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    1. Resnick, Sidney I., 1997. "Discussion of the Danish Data on Large Fire Insurance Losses," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 139-151, May.
    2. Beirlant, Jan & Teugels, Jozef L., 1992. "Modeling large claims in non-life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 11(1), pages 17-29, April.
    3. Arthur Charpentier & Emmanuel Flachaire, 2019. "Pareto Models for Top Incomes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02145024, HAL.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    5. Ana Cebrián & Michel Denuit & Philippe Lambert, 2003. "Generalized Pareto Fit to the Society of Actuaries’ Large Claims Database," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(3), pages 18-36.
    6. Liang Peng & Yongcheng Qi, 2004. "Estimating the First‐ and Second‐Order Parameters of a Heavy‐Tailed Distribution," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(2), pages 305-312, June.
    7. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    8. Joseph A. Schumpeter, 1949. "Vilfredo Pareto (1848–1923)," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 63(2), pages 147-173.
    9. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    10. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    11. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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