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

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 $O(\sqrt{\mathrm{\Delta }t}\log (1\mathrm{/}\mathrm{\Delta }t))$ via Donsker’s principle and linear algorithmic convergence of $(1-\kappa {)}^{2\mathrm{/}3}$; (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 $\mathrm{1,597}\times$ 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.