Extremal behavior of archimedean copulas

Martin Larsson*, Johanna Neslehova

*Corresponding author for this work

Publication: Scientific journalJournal articlepeer-review


We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

Original languageEnglish
Pages (from-to)195-216
Number of pages22
JournalAdvances in Applied Probability
Issue number1
Publication statusPublished - Mar 2011
Externally publishedYes


  • -norm symmetric distribution
  • Archimedean copula
  • Domain of attraction
  • Extreme value copula
  • Regular variation
  • Simplex distribution
  • Tail dependence
  • Threshold copula
  • Williamson transform

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