We develop a weak exact simulation technique for a process X defined by a multi-dimensional stochastic differential equation (SDE). Namely, for a Lipschitz function g, we propose a simulation based approximation of the expectation E[g(X_{t_1}, \cdots, X_{t_n})], which by-passes the...

We generalize the algorithm for semi-linear parabolic PDEs in Henry-Labordere to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution...

We extend the martingale version of the one-dimensional Brenier's theorem (Fr echet-Hoeffding coupling), established in Henry-Labord ere and Touzi to the infinitely-many marginals case. In short, their results give an explicit characterization of the optimal martingale transference plans as well...