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Risk Finance for Catastrophe Losses with Pareto‐Calibrated Lévy‐Stable Severities

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  • Michael R. Powers
  • Thomas Y. Powers
  • Siwei Gao

Abstract

For catastrophe losses, the conventional risk finance paradigm of enterprise risk management identifies transfer, as opposed to pooling or avoidance, as the preferred solution. However, this analysis does not necessarily account for differences between light‐ and heavy‐tailed characteristics of loss portfolios. Of particular concern are the decreasing benefits of diversification (through pooling) as the tails of severity distributions become heavier. In the present article, we study a loss portfolio characterized by nonstochastic frequency and a class of Lévy‐stable severity distributions calibrated to match the parameters of the Pareto II distribution. We then propose a conservative risk finance paradigm that can be used to prepare the firm for worst‐case scenarios with regard to both (1) the firm's intrinsic sensitivity to risk and (2) the heaviness of the severity's tail.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:riskan:v:32:y:2012:i:11:p:1967-1977
    DOI: 10.1111/j.1539-6924.2012.01906.x
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    References listed on IDEAS

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    1. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    2. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71(5), pages 421-421.
    3. Louis Anthony (Tony)Cox, 2008. "What's Wrong with Risk Matrices?," Risk Analysis, John Wiley & Sons, vol. 28(2), pages 497-512, April.
    4. Gao, Siwei & Powers, Michael R. & Chapman, Zaneta A., 2012. "A risk-based risk finance paradigm," Journal of Financial Transformation, Capco Institute, vol. 35, pages 173-178.
    5. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    6. Rustam Ibragimov & Dwight Jaffee & Johan Walden, 2009. "Nondiversification Traps in Catastrophe Insurance Markets," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 959-993, March.
    7. Samuelson, Paul A., 1967. "Efficient Portfolio Selection for Pareto-Lévy Investments*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(2), pages 107-122, June.
    8. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    9. Verlaak, Robert & Hürlimann, Werner & Beirlant, Jan, 2009. "Quasi-Likelihood Estimation of Benchmark Rates for Excess of Loss Reinsurance Programs," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 429-452, November.
    10. Rustam Ibragimov & Dwight Jaffee & Johan Walden, 2009. "Nondiversification Traps in Catastrophe Insurance Markets," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 959-993.
    11. 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.
    12. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    13. 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.
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    Cited by:

    1. Jo†Yu Wang & Wen†Lin Wu & Yang†Che Wu & Ming Jing Yang, 2017. "How To Manage Long†term Financial Self†sufficiency of a National Catastrophe Insurance Fund? The Feasibility of Three Bailout Programmes," European Financial Management, European Financial Management Association, vol. 23(5), pages 951-974, October.
    2. Yang‐Che Wu & Ming Jing Yang, 2018. "The effectiveness of asset, liability and equity hedging against catastrophe risk: the cases of winter storms in North America and Europe," European Financial Management, European Financial Management Association, vol. 24(5), pages 893-918, November.

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