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Tails of weakly dependent random vectors


  • Peter Tankov


We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mixture models, certain Archimedean copulas and extreme value copulas. The new measure allows to quantify the tail behavior of certain functionals of weakly dependent random vectors at the log scale.

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  • Peter Tankov, 2014. "Tails of weakly dependent random vectors," Papers 1402.4683,, revised Jan 2016.
  • Handle: RePEc:arx:papers:1402.4683

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    References listed on IDEAS

    1. 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.
    2. Enkelejd Hashorva & Jürg Hüsler, 2003. "On multivariate Gaussian tails," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 507-522, September.
    3. Asmussen, Søren & Rojas-Nandayapa, Leonardo, 2008. "Asymptotics of sums of lognormal random variables with Gaussian copula," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2709-2714, November.
    4. Wüthrich, Mario V., 2003. "Asymptotic Value-at-Risk Estimates for Sums of Dependent Random Variables," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 33(01), pages 75-92, May.
    5. Mainik, Georg & Embrechts, Paul, 2013. "Diversification in heavy-tailed portfolios: properties and pitfalls," Annals of Actuarial Science, Cambridge University Press, vol. 7(01), pages 26-45, March.
    6. Archil Gulisashvili & Peter Tankov, 2013. "Tail behavior of sums and differences of log-normal random variables," Papers 1309.3057,, revised Jan 2016.
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