L∞-measure of non-exchangeability for bivariate extreme value and Archimax copulas

AbstractIn the class of bivariate extreme value copulas, an upper bound is calculated for the measure of non-exchangeability μ∞ based on the L∞-norm distance between a copula C and its transpose Ct(x,y)=C(y,x). Copulas that are maximally non-exchangeable with respect to μ∞ are also determined. Moreover, similar upper bounds are given, respectively, for the class of all EV copulas having a fixed upper tail dependence coefficient and for the larger class of Archimax copulas