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arXiv · 2601.05290

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

Sri Sairam Gautam B
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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.

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Sri Sairam Gautam B. 2026-01-07. Multi-Period Martingale Optimal Transport: Classical Theory, Neural Acceleration, and Financial Applications. https://arxiv.org/abs/2601.05290

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