Copulas constructed from horizontal sections

Abstract

In analogy with the study of copulas whose diagonal sections have been fixed, we study the set $\mathcal{C}_h$ of copulas for which a horizontal section $h$ has been given. We first show that this set is not empty, by explicitly writing one such copula, which we call \textit{horizontal copula}. Then we find the copulas that bound both below and above the set $\mathcal{C}_h$. Finally we determine the expressions for Kendall's tau and Spearman's rho for the horizontal and the bounding copulas