Tail Properties of Multivariate Archimedean Copulas
Abstract
In this thesis, the tail properties of multivariate Archimedean copulas are investigated using known representation theorems involving L1-norm symmetric distributions and the Williamson d-transform. Several new results on the asymptotic properties of the Williamson d-transform are established and subsequently used to study the tails of Archimedean copulas. This makes it possible to recover many known results regarding their tail behavior in a straightforward and transparent way. In particular, coefficients of tail dependence, extreme value limits and threshold copulas are considered. A central theme is the emphasis on the probabilistic aspects of stochastic representations, rather than the analytic aspects of representations involving Archimedean generators.
Keywords
Cite
@article{arxiv.1008.1754,
title = {Tail Properties of Multivariate Archimedean Copulas},
author = {Martin Larsson},
journal= {arXiv preprint arXiv:1008.1754},
year = {2010}
}