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Numerical computation of martingale optimal transport on real line Guo, Gaoyue


We provide two numerical methods for solving the one dimensional martingale optimal transport problem, based respectively on the primal and dual problems. The first scheme considers the approximation of marginal distributions, through which the primal problem reduces to a linear optimisation problem. The second one aims at solving a minimisation problem $\psi\mapsto J(\psi)$ over the space of continuous functions $\psi: R\to R$ with linear growth, where $J$ involves some concave envelope and can be computed numerically. The second approach allows not only to solve the martingale optimal transport problem, but also to yield a family of approximating dual optimisers.

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