Sampling of probability measures in the convex order and approximation of Martingale Optimal Transport problems

In this paper, we propose sampling methods preserving the convex order between two probability measures. In particular, we introduce the Wasserstein projection of a first probability measure on the set of probability measures... [ view full abstract ]

In this paper, we propose sampling methods preserving the convex order between two probability measures. In particular, we introduce the Wasserstein projection of a first probability measure on the set of probability measures dominated by the second one for the convex order. We apply our techniques to approximate Martingale Optimal Transport problems with two of three marginals by using linear programming solvers.