Dual Attainment in Multi-Period Multi-Asset Martingale Optimal Transport and Its Computation

TL;DR

This paper proves the existence of dual optimizers in multi-asset, multi-period martingale optimal transport problems, extending duality theory and demonstrating practical computational methods for complex financial derivatives.

Contribution

It establishes dual attainment for general multi-asset, multi-period MOT problems, broadening theoretical understanding and providing computational techniques for high-dimensional cases.

Findings

Dual optimizers exist under mild conditions.

Numerical methods effectively solve large-scale MOT problems.

Validated approach with financial derivatives applications.

Abstract

We establish dual attainment for the multimarginal, multi-asset martingale optimal transport (MOT) problem, a fundamental question in the mathematical theory of model-independent pricing and hedging in quantitative finance. Our main result proves the existence of dual optimizers under mild regularity and irreducibility conditions, extending previous duality and attainment results from the classical and two-marginal settings to arbitrary numbers of assets and time periods. This theoretical advance provides a rigorous foundation for robust pricing and hedging of complex, path-dependent financial derivatives. To support our analysis, we present numerical experiments that demonstrate the practical solvability of large-scale discrete MOT problems using the state-of-the-art primal-dual linear programming (PDLP) algorithm. In particular, we solve multi-dimensional (or vectorial) MOT instances arising from the robust pricing of worst-of autocallable options, confirming the accuracy and feasibility of our theoretical results. Our work advances the mathematical understanding of MOT and highlights its relevance for robust financial engineering in high-dimensional and model-uncertain environments.