By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional...

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset and statically trade European call options for all possible strikes and finitely-many maturities. We present a general duality result which converts this problem...

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional...

We obtain bounds on the distribution of the maximum of a continuous martingale with fixed marginals at finitely many intermediate times. The bounds are sharp and attained by a solution to n-marginal Skorokhod embedding problem in Obloj and Spoida (2013). It follows that their embedding maximises...

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in cite{BeiglbockHenry-LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's...

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 consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset and statically trade European call options for all possible strikes and finitely-many maturities. We present a general duality result which converts this problem...

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod...

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...