On the class of truncation invariant bivariate copulas under constraints

We consider the class of bivariate copulas that are invariant under truncation with respect to the first variable. The elements of this class are hence characterized in terms of a suitable differential equation, which allows to express also their positive dependence properties. Various results about bounds for this class under special constraints are hence considered, with particular emphasis on the case when either the associated Spearman's ρ or Kendall's τ is known.