In this paper, motivated by the approximation of Martingale Optimal Transport problems, we are interested in sampling methods preserving the convex order for two probability measures µ and ν on ℝ<sup>d</sup>, with ν dominating µ. When (X<sub>i</sub>)1≤i≤I (resp. (Y<sub>j</sub>)1≤j≤J ) are independent and...