Paper: arXiv 2601.05290

Authors: Sri Sairam Gautam B

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 $O(\sqrt{Δt} \log(1/Δt))$ 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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous theoretical foundation for Multi-Period Martingale Optimal Transport alongside practical computational innovations. It combines strong analytical proofs (convergence rates via Donsker’s principle) with robust empirical validation across thousands of synthetic and real-world market scenarios, achieving significant online inference speedups.

Research Flowchart

  flowchart TD
    A["Research Goal: Efficient & Precise Computational Framework for Multi-Period Martingale Optimal Transport (MMOT)"] --> B["Inputs: Market Scenarios & Synthetic Dynamics (GBM, Merton, Heston)"]
    
    subgraph Methodology & Computation
        B --> C["Theoretical Foundations<br/>(Donsker Convergence & Adaptive Sparse Grids)"]
        C --> D["Hybrid Neural-Projection Solver<br/>(Transformer Warm-Starting + Newton-Raphson Projection)"]
    end

    D --> E["Pure Neural Solver: Real-Time Speedup<br/>(1,597x Faster Online Inference: 4.7s → 2.9ms)"]
    D --> F["Hybrid Solver: Precise Martingale Calibration<br/>(Ensures Constraints to 10⁻⁶ Precision)"]

    style A fill:#e1f5fe,stroke:#0288d1
    style D fill:#fff3e0,stroke:#f57c00
    style E fill:#e8f5e9,stroke:#388e3c
    style F fill:#e8f5e9,stroke:#388e3c