Concordance measure; Copula; Probability measure; Random vector

Based on the Scarsini axioms characterizing concordance measures between two random variables X and Y linked by a copula C, we introduce and discuss convex concordance measures. In their simplest form, they are dependent, except for a few degenerated cases, on a value of C at a single point (x, y) such that 0 < y < x < 21, and on the values at seven other points corresponding to this point, namely, (y, x), (x, 1 - y), (1 - y, x), (1 - x, y), (y, 1 - y), (1 - x, 1 - y) and (1 - y, 1 - x). Our approach covers, among others, such classical concordance measures as Spearman's rho, Gini's gamma, Blomqvist's beta, but also the concordance measures introduced by Fuchs and Schmidt. Though some of the introduced constructions are related to the results of Edwards, Mikusin`ski and Taylor, they offer a genuine motivation and provide a more transparent view.