On the structure of exchangeable extreme-value copulas

Jan-Frederik Mai; Matthias Scherer

doi:10.1016/j.jmva.2020.104670

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arXiv · 1909.09438

On the structure of exchangeable extreme-value copulas

Jan-Frederik Mai·Matthias Scherer

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Abstract

We show that the set of $d$-variate symmetric stable tail dependence functions, uniquely associated with exchangeable $d$-dimensional extreme-value copulas, is a simplex and determine its extremal boundary. The subset of elements which arises as $d$-margins of the set of $(d+k)$-variate symmetric stable tail dependence functions is shown to be proper for arbitrary $k \geq 1$. Finally, we derive an intuitive and useful necessary condition for a bivariate extreme-value copula to arise as bi-margin of an exchangeable extreme-value copula of arbitrarily large dimension, and thus to be conditionally iid.

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BibTeX RIS

Jan-Frederik Mai, Matthias Scherer. 2019-09-20. On the structure of exchangeable extreme-value copulas. https://doi.org/10.1016/j.jmva.2020.104670

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