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Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls

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

    (Tilburg University, Center for Economic Research)

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    Abstract

    Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution.For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to convergence of the corresponding lower tail dependence copulas to the Clayton copula.In this paper, these characterizations are refined and extended to the case of generators which are not necessarily continuously differentiable.Moreover, a counterexample is constructed showing that even if the generator of a strict Archimedean copula is continuously differentiable and slowly varying at the origin, then the lower tail dependence copulas do not need to converge to the independent copula.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2006-29.

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    Date of creation: 2006
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    Handle: RePEc:dgr:kubcen:200629

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    1. Alfred Müller & Marco Scarsini, 2003. "Archimedean Copulae and Positive Dependence," ICER Working Papers - Applied Mathematics Series 25-2003, ICER - International Centre for Economic Research.
    2. Bassan, Bruno & Spizzichino, Fabio, 2005. "Bivariate survival models with Clayton aging functions," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 6-12, August.
    3. Klugman, Stuart A. & Parsa, Rahul, 1999. "Fitting bivariate loss distributions with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 139-148, March.
    4. Juri, Alessandro & Wuthrich, Mario V., 2002. "Copula convergence theorems for tail events," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 405-420, June.
    5. Charpentier, A. & Segers, J.J.J., 2006. "Convergence of Archimedean Copulas," Discussion Paper 2006-28, Tilburg University, Center for Economic Research.
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    Cited by:
    1. Charpentier, Arthur & Segers, Johan, 2008. "Convergence of Archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 412-419, March.

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