Tail Properties of Multivariate Archimedean Copulas

Martin Larsson

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arXiv · 1008.1754

Tail Properties of Multivariate Archimedean Copulas

Martin Larsson

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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.

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Martin Larsson. 2010-08-10. Tail Properties of Multivariate Archimedean Copulas. https://arxiv.org/abs/1008.1754

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