On Extreme Value Copulas with Given Concordance Measures

Abstract

The dependence measures, like for example Kendall tau, Spearman rho, Blomquist beta or tail dependence coefficient, are the main numerical characterization of Bivariate Extreme Value Copulas. Such copulas are characterized by a function on the unit segment, called a Pickands dependence function, which is convex and comprised between two bounds. We identify the smallest possible compact sets containing the graphs of all Pickands dependence functions whose corresponding bivariate extreme-value copula has fixed values of given dependence measures. Moreover we provide the bounds for such bivariate extreme-value copulas.