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Paths And Indices Of Maximal Tail Dependence

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  • Furman, Edward
  • Su, Jianxi
  • Zitikis, Ričardas

Abstract

We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the context of both symmetric and asymmetric copulas with and without singularities. As a remedy, we introduce a notion of paths of maximal (tail) dependence and utilize the notion to propose several new indices of tail dependence. The suggested new indices are conservative, conform with the basic concepts of modern quantitative risk management, and are capable of differentiating between distinct risky positions in situations when the existing indices fail to do so.

Suggested Citation

  • Furman, Edward & Su, Jianxi & Zitikis, Ričardas, 2015. "Paths And Indices Of Maximal Tail Dependence," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 661-678, September.
    • Handle: RePEc:cup:astinb:v:45:y:2015:i:03:p:661-678_00
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    Citations

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    Cited by:

    1. Xin Liu & Jiang Wu & Chen Yang & Wenjun Jiang, 2018. "A Maximal Tail Dependence-Based Clustering Procedure for Financial Time Series and Its Applications in Portfolio Selection," Risks, MDPI, vol. 6(4), pages 1-26, October.
    2. Francesca Mariani & Gloria Polinesi & Maria Cristina Recchioni, 2022. "A tail-revisited Markowitz mean-variance approach and a portfolio network centrality," Computational Management Science, Springer, vol. 19(3), pages 425-455, July.
    3. Furman, Edward & Kuznetsov, Alexey & Su, Jianxi & Zitikis, Ričardas, 2016. "Tail dependence of the Gaussian copula revisited," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 97-103.
    4. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Copulas and related properties," Papers 1610.02126, arXiv.org.
    5. Hua, Lei & Polansky, Alan & Pramanik, Paramahansa, 2019. "Assessing bivariate tail non-exchangeable dependence," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    6. Paramahansa Pramanik, 2024. "Dependence on Tail Copula," J, MDPI, vol. 7(2), pages 1-26, April.
    7. Li, Xiaoting & Joe, Harry, 2024. "Multivariate directional tail-weighted dependence measures," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    8. Vadim Semenikhine & Edward Furman & Jianxi Su, 2018. "On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance," Risks, MDPI, vol. 6(3), pages 1-20, August.
    9. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Copulas and related properties," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 109-121.
    10. Jiandong Ren & Kristina Sendova & Ričardas Zitikis, 2019. "Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”," Risks, MDPI, vol. 7(3), pages 1-7, September.

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