Multi-Period Martingale Optimal Transport: Classical Theory, Neural Acceleration, and Financial Applications

Abstract

This paper develops a computational framework for Multi-Period Martingale Optimal Transport (MMOT), addressing convergence rates, algorithmic efficiency, and financial calibration. Our contributions include: (1) Theoretical analysis: We establish discrete convergence rates of $O(\sqrt{\hat{I}”t}\log (1/\hat{I}”t))$ via Donsker's principle and linear algorithmic convergence of $(1-\hat{I}º{)}^{2/3}$; (2) Algorithmic improvements: We introduce incremental updates ($O(M^2)$ complexity) and adaptive sparse grids; (3) Numerical implementation: A hybrid neural-projection solver is proposed, combining transformer-based warm-starting with Newton-Raphson projection. Once trained, the pure neural solver achieves a $1,597\times$ online inference speedup ($4.7$s $\to 2.9$ms) suitable for real-time applications, while the hybrid solver ensures martingale constraints to $10^{-6}$ precision. Validated on 12,000 synthetic instances (GBM, Merton, Heston) and 120 real market scenarios.

This preprint is being withdrawn by the authors. We identified errors in the reference list, including incorrect attribution of works to authors -- references and were cited inaccurately with wrong author arrangements and publication details. We are withdrawing the manuscript to correct these errors before any further dissemination. We apologize for the oversight