Before revision: The improved Fr\'echet--Hoeffding bounds are ad-hoc estimates on the Fr\'echet class of probability distributions with given marginals and prescribed values on a subset of R d . Using an optimal transport approach, we first provide an alternative derivation of the improved upper bound.
After revision: Motivated by applications in model-free finance and quantitative risk management, we consider Fr\'echet class of probability distributions with given marginals and prescribed values on a subset of R d . Using an optimal transport approach, we first provide an alternative derivation of the improved upper bound.