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

2026/01/07 by Sri Sairam Gautam B · 1 voice
Economics, Econometrics and Finance · #q-fin.CP #q-fin.MF #q-fin.PR

paper · pdf

arxiv published 2026/01/07 · arxiv updated 2026/04/19

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(√(Δt) log(1/Δt)) via Donsker's principle and linear algorithmic convergence of (1-κ)^2/3; (2) Algorithmic improvements: We introduce incremental updates (O(M²) 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× online inference speedup (4.7s → 2.9ms) 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.

Citations

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Discussions

• Sri Sairam Gautam B: Multi-Period Martingale Optimal Transport: Classical Theory, Neural Acceleration, and Financial Applications https://arxiv.org/abs/2601.05290 https://arxiv.org/pdf/2601.05290 http [bsky, 0 points, 0 comments]

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