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Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness

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  • Embrechts, Paul
  • Neslehová, Johanna
  • Wüthrich, Mario V.
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    Abstract

    Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the switch from a finite to an infinite mean model gives a completely different asymptotic behaviour. Our main result proves a conjecture made in Barbe et al. [Barbe, P., Fougères, A.L., Genest, C., 2006. On the tail behavior of sums of dependent risks. ASTIN Bull. 36(2), 361-374].

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 44 (2009)
    Issue (Month): 2 (April)
    Pages: 164-169

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    Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:164-169

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Value-at-Risk Subadditivity Dependence structure Archimedean copula Aggregation;

    References

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    1. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers dp549, Financial Markets Group.
    2. Wei, Gang & Hu, Taizhong, 2002. "Supermodular dependence ordering on a class of multivariate copulas," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 375-385, May.
    3. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    4. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    5. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    6. 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.
    7. J. Dhaene & R. J. A. Laeven & S. Vanduffel & G. Darkiewicz & M. J. Goovaerts, 2008. "Can a Coherent Risk Measure Be Too Subadditive?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 365-386.
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    Citations

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    Cited by:
    1. Suzanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures," Post-Print hal-00921283, HAL.
    2. Lv, Wenhua & Pan, Xiaoqing & Hu, Taizhong, 2013. "Asymptotics of the risk concentration based on the tail distortion risk measure," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2703-2710.
    3. Chen, Die & Mao, Tiantian & Pan, Xiaoqing & Hu, Taizhong, 2012. "Extreme value behavior of aggregate dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 99-108.
    4. 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 Dec 2013.
    5. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    6. 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.
    7. Pavel V. Shevchenko, 2009. "Implementing Loss Distribution Approach for Operational Risk," Papers 0904.1805, arXiv.org, revised Jul 2009.
    8. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 273-280.
    9. Chen Zou, 2009. "Dependence structure of risk factors and diversification effects," DNB Working Papers 219, Netherlands Central Bank, Research Department.
    10. Mao, Tiantian & Lv, Wenhua & Hu, Taizhong, 2012. "Second-order expansions of the risk concentration based on CTE," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 449-456.

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