Absolutely continuous copulas obtained by regularization of the   Frech\'{e}t--Hoeffding bounds
  We show that the lower and upper Frech\'{e}t-Hoeffding copulas, which are singular, can be regularized to absolutely continuous copulas. The method, which is constructive and explicit, states sufficient conditions for when an absolutely continuous copula can be achieved by averaging. A higher degree of regularisation cannot be achieved with the proposed method. 
Oscar Bj\"ornham, Niklas Br\"annstr\"om and Leif Persson
math.PR