On the structure of exchangeable extreme-value copulas

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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.