IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03186680.html
   My bibliography  Save this paper

Pareto Models for Risk Management

Author

Listed:
  • Arthur Charpentier

    (UQAM - Université du Québec à Montréal = University of Québec in Montréal)

  • Emmanuel Flachaire

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

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, derive formulas for various measures and indices, and finally provide applications on insurance losses and financial risks.

Suggested Citation

  • Arthur Charpentier & Emmanuel Flachaire, 2021. "Pareto Models for Risk Management," Post-Print hal-03186680, HAL.
    • Handle: RePEc:hal:journl:hal-03186680
    DOI: 10.1007/978-3-030-54252-8_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    3. 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.
    4. 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.
    5. Arthur Charpentier & Emmanuel Flachaire, 2019. "Pareto Models for Top Incomes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02145024, HAL.
    6. 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.
    7. 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.
    8. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    9. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    2. S. A. Abu Bakar & Saralees Nadarajah & Z. A. Absl Kamarul Adzhar, 2018. "Loss modeling using Burr mixtures," Empirical Economics, Springer, vol. 54(4), pages 1503-1516, June.
    3. A. B. Atkinson, 2017. "Pareto and the Upper Tail of the Income Distribution in the UK: 1799 to the Present," Economica, London School of Economics and Political Science, vol. 84(334), pages 129-156, April.
    4. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," International Journal of Forecasting, Elsevier, vol. 33(4), pages 958-969.
    5. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
    6. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
    7. Cirillo, Pasquale, 2013. "Are your data really Pareto distributed?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5947-5962.
    8. Goran Andjelic & Ivana Milosev & Vladimir Djakovic, 2010. "Extreme Value Theory In Emerging Markets," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 55(185), pages 63-106, April - J.
    9. Arthur Charpentier & Emmanuel Flachaire, 2022. "Pareto models for top incomes and wealth," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(1), pages 1-25, March.
    10. Kittiya Chaithep & Songsak Sriboonchitta & Chukiat Chaiboonsri & Pathairat Pastpipatkul, 2012. "Value at Risk Analysis of Gold Price Returns Using Extreme Value Theory," The Empirical Econometrics and Quantitative Economics Letters, Faculty of Economics, Chiang Mai University, vol. 1(4), pages 151-168, December.
    11. Zhi-Fu Mi & Yi-Ming Wei & Bao-Jun Tang & Rong-Gang Cong & Hao Yu & Hong Cao & Dabo Guan, 2017. "Risk assessment of oil price from static and dynamic modelling approaches," Applied Economics, Taylor & Francis Journals, vol. 49(9), pages 929-939, February.
    12. Madhusudan Karmakar, 2013. "Estimation of tail‐related risk measures in the Indian stock market: An extreme value approach," Review of Financial Economics, John Wiley & Sons, vol. 22(3), pages 79-85, September.
    13. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    14. Weshah Razzak, "undated". "On the GCC Currency Union," API-Working Paper Series 0910, Arab Planning Institute - Kuwait, Information Center.
    15. Athanasios Sachlas & Takis Papaioannou, 2014. "Residual and Past Entropy in Actuarial Science and Survival Models," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 79-99, March.
    16. Dr. Ibrahim Onour, "undated". "The Global Financial Crisis and Equity Markets in Middle East Oil Exporting Countries," API-Working Paper Series 1009, Arab Planning Institute - Kuwait, Information Center.
    17. Bernard, Carole & Kazzi, Rodrigue & Vanduffel, Steven, 2020. "Range Value-at-Risk bounds for unimodal distributions under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 9-24.
    18. Henry Lam & Clementine Mottet, 2017. "Tail Analysis Without Parametric Models: A Worst-Case Perspective," Operations Research, INFORMS, vol. 65(6), pages 1696-1711, December.
    19. Michael R. Powers & Thomas Y. Powers & Siwei Gao, 2012. "Risk Finance for Catastrophe Losses with Pareto‐Calibrated Lévy‐Stable Severities," Risk Analysis, John Wiley & Sons, vol. 32(11), pages 1967-1977, November.
    20. Bhattacharyya, Malay & Ritolia, Gopal, 2008. "Conditional VaR using EVT - Towards a planned margin scheme," International Review of Financial Analysis, Elsevier, vol. 17(2), pages 382-395.

    More about this item

    Keywords

    EPD; expected shortfall; financial risks; GPD; hill; pareto; quantile; rare events; regular variation; reinsurance; second order; value-at-risk;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-03186680. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.