Multi-Period Martingale Optimal Transport: Classical Theory, Neural Acceleration, and Financial Applications
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917419448008704 |
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| author | B, Sri Sairam Gautam |
| author_facet | B, Sri Sairam Gautam |
| contents | 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 $O(\sqrt{Δt} \log(1/Δt))$ via Donsker's principle and linear algorithmic convergence of $(1-κ)^{2/3}$; (2) Algorithmic improvements: We introduce incremental updates ($O(M^2)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05290 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-Period Martingale Optimal Transport: Classical Theory, Neural Acceleration, and Financial Applications B, Sri Sairam Gautam Computational Finance Mathematical Finance Pricing of Securities 90C25, 60G42, 91G20, 49Q22, 65K10 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 $O(\sqrt{Δt} \log(1/Δt))$ via Donsker's principle and linear algorithmic convergence of $(1-κ)^{2/3}$; (2) Algorithmic improvements: We introduce incremental updates ($O(M^2)$ 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. |
| title | Multi-Period Martingale Optimal Transport: Classical Theory, Neural Acceleration, and Financial Applications |
| topic | Computational Finance Mathematical Finance Pricing of Securities 90C25, 60G42, 91G20, 49Q22, 65K10 |
| url | https://arxiv.org/abs/2601.05290 |