Reflection invariant copulas.

Abstract In the present paper we study the class of all those copulas that are invariant under a special class of transformations, called reflections. In particular, we focus on the special role played by the independence copula within this class. For this purpose, we introduce a bijective transformation which turns every copula into a reflection invariant copula and enforces a strong geometric property: The n -fold composition of this transformation to a d -dimensional copula coincides with the independence copula on the mesh { 0 , 1 2 n ,... , 2 n − 1 2 n , 1 } d. It turns out that the independence copula is the unique fixed point of the introduced transformation. [ABSTRACT FROM AUTHOR]