Extremal behavior of archimedean copulas

Martin Larsson*, Johanna Neslehova

*Korrespondierende*r Autor*in für diese Arbeit

Publikation: Wissenschaftliche FachzeitschriftOriginalbeitrag in FachzeitschriftBegutachtung

Abstract

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.

OriginalspracheEnglisch
Seiten (von - bis)195-216
Seitenumfang22
FachzeitschriftAdvances in Applied Probability
Jahrgang43
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - März 2011
Extern publiziertJa

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