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Diversification benefits under multivariate second order regular variation

Author

Listed:
  • Das, Bikramjit

    (Singapore University of Technology and Design)

  • Kratz, Marie

    (ESSEC Research Center, ESSEC Business School)

Abstract

We analyze risk diversification in a portfolio of heavy-tailed risk factors under the assumption of second order multivariate regular variation. Asymptotic limits for a measure of diversification benefit are obtained when considering, for instance, the value-at-risk . The asymptotic limits are computed in a few examples exhibiting a variety of different assumptions made on marginal or joint distributions. This study ties up existing related results available in the literature under a broader umbrella.

Suggested Citation

  • Das, Bikramjit & Kratz, Marie, 2017. "Diversification benefits under multivariate second order regular variation," ESSEC Working Papers WP1706, ESSEC Research Center, ESSEC Business School.
    • Handle: RePEc:ebg:essewp:dr-17006
    as

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    References listed on IDEAS

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    1. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
    2. Hua, Lei & Joe, Harry, 2011. "Second order regular variation and conditional tail expectation of multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 537-546.
    3. Grant B. Weller & Daniel Cooley, 2014. "A sum characterization of hidden regular variation with likelihood inference via expectation-maximization," Biometrika, Biometrika Trust, vol. 101(1), pages 17-36.
    4. Ibragimov, Rustam & Jaffee, Dwight & Walden, Johan, 2011. "Diversification disasters," Journal of Financial Economics, Elsevier, vol. 99(2), pages 333-348, February.
    5. Tong, Bin & Wu, Chongfeng & Xu, Weidong, 2012. "Risk concentration of aggregated dependent risks: The second-order properties," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 139-149.
    6. Degen, Matthias & Lambrigger, Dominik D. & Segers, Johan, 2010. "Risk concentration and diversification: Second-order properties," LIDAM Reprints ISBA 2010011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Degen, Matthias & Lambrigger, Dominik D. & Segers, Johan, 2010. "Risk concentration and diversification: Second-order properties," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 541-546, June.
    8. Alink, Stan & Lowe, Matthias & V. Wuthrich, Mario, 2004. "Diversification of aggregate dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 77-95, August.
    9. Omey, E. & Willekens, E., 1986. "Second order behaviour of the tail of a subordinated probability distribution," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 339-353, February.
    10. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
    11. Barbe, Philippe & Fougères, Anne-Laure & Genest, Christian, 2006. "On the Tail Behavior of Sums of Dependent Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 361-373, November.
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    More about this item

    Keywords

    asymptotic theory; diversification benefit; heavy tail; risk concentration; second order regular variation; value-at-risk;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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