Computational Methods for Martingale Optimal Transport Problems

We develop numerical methods for solving the martingale optimal transport (MOT) problem. We prove that the MOT problem can be approximated through a sequence of linear programming (LP) problems which result from a... [ view full abstract ]

We develop numerical methods for solving the martingale optimal transport (MOT) problem. We prove that the MOT problem can be approximated through a sequence of linear programming (LP) problems which result from a discretisation of the marginal distributions combined with a suitable relaxation of the martingale constraint. Specialising to the one-step model in dimension one, we provide an estimation on the convergence rate.

We adopt two computational algorithms to solve the LP problem that is related to a tailored discretisation of the marginals preserving the increasing convex order, based respectively on the iterative Bregman projection and stochastic averaged gradient method.