Distributionally Robust Martingale Optimal Transport

TL;DR

This paper introduces a distributionally robust variant of martingale optimal transport, providing a finite-sample approximation method with error bounds, motivated by financial super-hedging applications.

Contribution

It formulates a relaxed MOT problem with distributional uncertainty and develops a linear programming approximation with quantifiable error bounds.

Findings

Approximation error is $O(n^{-1/2})$ with respect to sample size.

The approach is applicable to path-dependent expectations in finance.

Provides a practical computational framework for robust super-hedging.

Abstract

We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark marginal distributions. This problem is a relaxation of the martingale optimal transport (MOT) problem and is motivated by applications to super-hedging in financial markets. We show that the empirical version of our relaxed MOT problem can be approximated within $O\left( n^{-1/2}\right)$ error where $n$ is the number of samples of each of the individual marginal distributions (generated independently) and using a suitably constructed finite-dimensional linear programming problem.