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Tail asymptotic results for elliptical distributions

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  • Hashorva, Enkelejd

Abstract

Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability and the conditional probability , for x,y large.

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  • Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:158-164
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    References listed on IDEAS

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    1. Schmidt, Rafael & Schmieder, Christian, 2009. "Modelling dynamic portfolio risk using risk drivers of elliptical processes," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 229-244, April.
    2. Asimit, Alexandru V. & Jones, Bruce L., 2007. "Extreme behavior of bivariate elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 53-61, July.
    3. Hashorva, Enkelejd, 2005. "Elliptical triangular arrays in the max-domain of attraction of Hüsler-Reiss distribution," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 125-135, April.
    4. Szablowski, Pawel J., 1998. "Uniform Distributions on Spheres in Finite DimensionalL[alpha]and Their Generalizations," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 103-117, February.
    5. 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.
    6. Berman, Simeon M., 1983. "Sojourns and extremes of Fourier sums and series with random coefficients," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 213-238, August.
    7. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    8. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    2. Lorenzo Ricci & David Veredas, 2012. "TailCoR," Working Papers 1227, Banco de España.
      • Sla{dj}ana Babi'c & Christophe Ley & Lorenzo Ricci & David Veredas, 2020. "TailCoR," Papers 2011.14817, arXiv.org.
    3. Manner, Hans & Segers, Johan, 2011. "Tails of correlation mixtures of elliptical copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 153-160, January.

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