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

Paper: arXiv 2602.02996

Authors: Charlie Che, Tongseok Lim, Yue Sun

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.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly complex theoretical proof of dual attainment in multi-period, multi-asset martingale optimal transport (MOT), solving a major open problem in mathematical finance. While it includes numerical validation via the PDLP algorithm applied to autocallable options, the focus is overwhelmingly theoretical with synthetic numerical setups rather than extensive empirical backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Prove Dual Attainment for Multi-Period Multi-Asset MOT] --> B[Set Up Theoretical Framework & Irreducibility Conditions]
    B --> C[Inputs: Financial Derivatives & Asset Marginals]
    C --> D[Formulate Discretized Primal-Dual MOT Problem]
    D --> E[Computational Process: Solve via Primal-Dual LP Algorithm]
    E --> F[Outcomes: Rigorous Proof of Dual Attainment & Practical Robust Hedging for Complex Derivatives]