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Convergence of Archimedean Copulas

Author

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  • Charpentier, A.
  • Segers, J.J.J.

    (Tilburg University, Center For Economic Research)

Abstract

Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Charpentier, A. & Segers, J.J.J., 2006. "Convergence of Archimedean Copulas," Discussion Paper 2006-28, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:410237d0-4c38-48f6-8f36-685b335f9e6b
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/777850/28.pdf
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    References listed on IDEAS

    as
    1. Juri, Alessandro & Wuthrich, Mario V., 2002. "Copula convergence theorems for tail events," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 405-420, June.
    2. Barbe, Philippe & Genest, Christian & Ghoudi, Kilani & Rémillard, Bruno, 1996. "On Kendall's Process," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 197-229, August.
    3. Charpentier, Arthur & Segers, Johan, 2007. "Lower tail dependence for Archimedean copulas: Characterizations and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 525-532, May.
    4. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    5. Charpentier, A. & Segers, J.J.J., 2006. "Lower Tail Dependence for Archimedean Copulas : Characterizations and Pitfalls," Other publications TiSEM ae669e5a-1929-42d9-b137-6, Tilburg University, School of Economics and Management.
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    Citations

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    Cited by:

    1. Henryk Zähle, 2022. "A concept of copula robustness and its applications in quantitative risk management," Finance and Stochastics, Springer, vol. 26(4), pages 825-875, October.
    2. Włodzimierz Wysocki, 2015. "Kendall's tau and Spearman's rho for n -dimensional Archimedean copulas and their asymptotic properties," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 442-459, December.
    3. Charpentier, Arthur & Segers, Johan, 2007. "Lower tail dependence for Archimedean copulas: Characterizations and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 525-532, May.
    4. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
    5. Wysocki, Włodzimierz, 2012. "Constructing archimedean copulas from diagonal sections," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 818-826.
    6. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 223-256, August.
    7. Charpentier, A. & Segers, J.J.J., 2006. "Lower Tail Dependence for Archimedean Copulas : Characterizations and Pitfalls," Other publications TiSEM ae669e5a-1929-42d9-b137-6, Tilburg University, School of Economics and Management.
    8. Wysocki, Włodzimierz, 2013. "When a copula is archimax," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 37-45.

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    More about this item

    Keywords

    Archimedean copula; generator; Kendall distribution function;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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