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

TL;DR

This paper introduces a comprehensive computational framework for Multi-Period Martingale Optimal Transport, combining theoretical convergence analysis, algorithmic enhancements, and a neural-based solver for efficient financial applications.

Contribution

It provides new theoretical convergence rates, algorithmic improvements, and a hybrid neural-projection solver for MMOT, enabling real-time financial computations.

Findings

Theoretical convergence rate of $O(\sqrt{\Delta t} \log(1/\Delta t))$ established.

Neural solver achieves 1,597x speedup in inference time.

Hybrid solver maintains martingale constraints to $10^{-6}$ accuracy.

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 $O(\sqrt{\Delta t} \log(1/\Delta t))$ via Donsker's principle and linear algorithmic convergence of $(1-\kappa)^{2/3}$; (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.