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

2026-02-03

AI Summary

This study addresses the dual attainment of multi-period, multi-asset martingale optimal transport (MOT) problems, providing a theoretical foundation for model-free pricing and hedging of path-dependent derivatives. Under mild regularity and irreducibility conditions, it extends the existence of dual optimizers—previously established only for classical and two-marginal settings—to an arbitrary number of assets and time periods. The approach combines duality-theoretic analysis with state-of-the-art primal-dual linear programming (PDLP) algorithms to enable efficient computation of large-scale discrete MOT problems. Numerical experiments demonstrate the method’s accuracy and practical feasibility through high-dimensional applications, including worst-of autocallable options.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• martingale optimal transport
• dual attainment
• multi-period
• multi-asset
• model-independent pricing

Innovation

• martingale optimal transport
• dual attainment
• multi-asset
• multi-period
• robust pricing