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Analysis of the Expected Shortfall of Aggregate Dependent Risks

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  • Alink, Stan
  • Löwe, Matthias
  • Wüthrich, Mario V.

Abstract

We consider d identically and continuously distributed dependent risks X1,…, Xd. Our main result is a theorem on the asymptotic behaviour of expected shortfall for the aggregate risks: there is a constant cd such that for large u we have . Moreover we study diversification effects in two dimensions, similar to our Value-at-Risk studies in [2].

Suggested Citation

  • Alink, Stan & Löwe, Matthias & Wüthrich, Mario V., 2005. "Analysis of the Expected Shortfall of Aggregate Dependent Risks," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 25-43, May.
    • Handle: RePEc:cup:astinb:v:35:y:2005:i:01:p:25-43_01
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    Cited by:

    1. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    2. Georg Mainik & Ludger Ruschendorf, 2010. "Ordering of multivariate probability distributions with respect to extreme portfolio losses," Papers 1010.5171, arXiv.org.
    3. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    4. Biard, Romain & Lefèvre, Claude & Loisel, Stéphane, 2008. "Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 412-421, December.
    5. Woo, Jae-Kyung, 2016. "On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delays," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 354-363.
    6. Charpentier, Arthur & Segers, Johan, 2009. "Tails of multivariate Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1521-1537, August.
    7. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    8. Mainik Georg & Rüschendorf Ludger, 2012. "Ordering of multivariate risk models with respect to extreme portfolio losses," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 73-106, March.
    9. 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.
    10. 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.
    11. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    12. Cuberos A. & Masiello E. & Maume-Deschamps V., 2015. "High level quantile approximations of sums of risks," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-18, October.
    13. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
    14. 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.

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