Nested Optimal Transport Distances

ArXiv ID: 2509.06702 “View on arXiv”

Authors: Ruben Bontorno, Songyan Hou

Abstract

Simulating realistic financial time series is essential for stress testing, scenario generation, and decision-making under uncertainty. Despite advances in deep generative models, there is no consensus metric for their evaluation. We focus on generative AI for financial time series in decision-making applications and employ the nested optimal transport distance, a time-causal variant of optimal transport distance, which is robust to tasks such as hedging, optimal stopping, and reinforcement learning. Moreover, we propose a statistically consistent, naturally parallelizable algorithm for its computation, achieving substantial speedups over existing approaches.

Keywords: Optimal Transport, Generative Models, Time Series Simulation, Hedging, Reinforcement Learning

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced optimal transport theory and stochastic calculus with dense mathematical notation, including definitions, propositions, and convergence theorems. It includes rigorous empirical validation with code-ready algorithms, statistical convergence tests, and benchmarking against theoretical values on synthetic financial processes.

  flowchart TD
    A["Research Goal<br>Evaluate generative models for financial time series<br>in decision-making tasks"] --> B["Key Methodology<br>Nested Optimal Transport Distance<br>time-causal & robust to hedging/RL"]
    B --> C["Data Inputs<br>Financial time series datasets<br>e.g., stock prices"]
    C --> D["Computational Process<br>Statistically consistent, parallelizable algorithm<br>for efficient computation"]
    D --> E["Key Findings & Outcomes<br>Substantial speedups over existing approaches<br>Validated for hedging, optimal stopping, RL"]