In the framework of Galichon, Henry-Labordère and Touzi, we consider the model-free no-arbitrage bound of variance option given the marginal distributions of the underlying asset. We first make some approximations which restrict the computation on a bounded domain. Then we propose a gradient...

In the framework of Galichon, Henry-Labordère and Touzi, we consider the model-free no-arbitrage bound of variance option given the marginal distributions of the underlying asset. We first make some approximations which restrict the computation on a bounded domain. Then we propose a gradient...

In their paper [2], Carmona and Touzi have studied an optimal multiple stopping time problem in a market where the price process is continuous. In this paper, we generalize their results when the price process is allowed to jump. Also, we generalize the problem associated to the valuation of...

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 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 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...