On the structure of exchangeable extreme-value copulas

We show that the set of d-variate symmetric stable tail dependence functions is a simplex and we 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 >= 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. (C) 2020 Elsevier Inc. All rights reserved.