Title: Markov product invariance in classes of bivariate copulas characterized by univariate functions
Authors: Marco Tschimpke - Paris Lodron University Salzburg (Austria) [presenting]
Wolfgang Trutschnig - University of Salzburg (Austria)
Juan Fernandez Sanchez - Universidad de Almeria (Spain)
Abstract: The aim is to extend and sharpen some results concerning the notion of Markov product idempotence in some well-known classes of copulas. Focusing on families of copulas which are characterized by univariate functions we show that in the class of extreme-value copulas, in the class of diagonal copulas and in some special class of copulas represented by measure-preserving transformations only the usual suspects (if contained in the class) are idempotent, namely the product copula $\Pi$ and minimum copula $M$. Additionally, we prove the conjecture that the only idempotent Archimedean copula is the product copula $\Pi$.