Absolutely continuous copulas with given sub-diagonal section

Recently, Durante and Jaworski (2008) [6] have proved that the class of absolutely continuous copulas with a given diagonal section is non-empty in case that the diagonal function is such that the set of points where this coincides with the identity function has null-measure. In this paper, we show that if we consider sub-diagonals (or super-diagonals), then the framework changes. Concretely, for each sub-diagonal function there exists an absolutely continuous copula having this function as sub-diagonal section.