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Gaussian approximation of conditional elliptical copulas

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  • Hashorva, Enkelejd
  • Jaworski, Piotr

Abstract

In this paper the limits of elliptical copulas under univariate conditioning are characterized, allowing for the conditioning random variable to have a rapidly varying tail. Further, we investigate the quality of approximation by imposing some weak asymptotic restrictions.

Suggested Citation

  • Hashorva, Enkelejd & Jaworski, Piotr, 2012. "Gaussian approximation of conditional elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 397-407.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:397-407
    DOI: 10.1016/j.jmva.2012.04.017
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    References listed on IDEAS

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    1. 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.
    2. Wolfgang Bischoff & Frank Miller & Enkelejd Hashorva & Jürg Hüsler, 2003. "Asymptotics of a Boundary Crossing Probability of a Brownian Bridge with General Trend," Methodology and Computing in Applied Probability, Springer, vol. 5(3), pages 271-287, September.
    3. Wolfgang Härdle & Ostap Okhrin, 2010. "De copulis non est disputandum," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(1), pages 1-31, March.
    4. Donnelly, Catherine & Embrechts, Paul, 2010. "The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 1-33, May.
    5. Juri, Alessandro & Wuthrich, Mario V., 2002. "Copula convergence theorems for tail events," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 405-420, June.
    6. Durante, Fabrizio & Foschi, Rachele & Spizzichino, Fabio, 2008. "Threshold copulas and positive dependence," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2902-2909, December.
    7. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
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    Cited by:

    1. Hashorva, Enkelejd, 2019. "Approximation of some multivariate risk measures for Gaussian risks," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 330-340.
    2. Jaworski, Piotr, 2015. "Univariate conditioning of vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 89-103.
    3. Ling, Chengxiu, 2019. "Asymptotics of multivariate conditional risk measures for Gaussian risks," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 205-215.
    4. E. Hashorva, 2018. "Approximation of Some Multivariate Risk Measures for Gaussian Risks," Papers 1803.06922, arXiv.org, revised Oct 2018.

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