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Diversification for general copula dependence

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  • Stan Alink
  • Matthias Löwe
  • Mario V. Wüthrich

Abstract

We generalize the extreme value analysis for Archimedean copulas (see Alink, Löwe and Wüthrich, 2003) to the non‐Archimedean case: Assume we have d≥2 exchangeable and continuously distributed risks X1,…,Xd. Under appropriate assumptions there is a constant qd such that, for all large u, we have . The constant qd describes the asymptotic dependence structure. Typically, qd will depend on more aspects of this dependence structure than the well‐known tail dependence coefficient.

Suggested Citation

  • Stan Alink & Matthias Löwe & Mario V. Wüthrich, 2007. "Diversification for general copula dependence," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 446-465, November.
    • Handle: RePEc:bla:stanee:v:61:y:2007:i:4:p:446-465
    DOI: 10.1111/j.1467-9574.2007.00370.x
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    Cited by:

    1. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    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. 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.
    4. Dhaene, Jan & Denuit, Michel & Vanduffel, Steven, 2009. "Correlation order, merging and diversification," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 325-332, December.
    5. Asimit, Alexandru V. & Gerrard, Russell, 2016. "On the worst and least possible asymptotic dependence," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 218-234.
    6. Hua, Lei & Joe, Harry, 2012. "Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 492-503.
    7. 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.
    8. 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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