A note on Archimax copulas and their representation by means of conic copulas

The aim of this note is to prove the equivalence between the class of conic copulas and the class of Archimax copulas based on the lower Fréchet-Hoeffding bound W. We demonstrate the transition from arbitrary conic copula to appropriate Pickands dependence function, and vice-versa. Our results show that Archimax copulas are isomorphic transforms of either EV-copulas or conic copulas.