Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 43, Number 1 (2011), 195-216.
Extremal behavior of Archimedean copulas
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.
Adv. in Appl. Probab., Volume 43, Number 1 (2011), 195-216.
First available in Project Euclid: 15 March 2011
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Larsson, Martin; Nešlehová, Johanna. Extremal behavior of Archimedean copulas. Adv. in Appl. Probab. 43 (2011), no. 1, 195--216. doi:10.1239/aap/1300198519. https://projecteuclid.org/euclid.aap/1300198519