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arXiv · 2509.06702

Nested Optimal Transport Distances

Ruben Bontorno·Songyan Hou
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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.

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Ruben Bontorno, Songyan Hou. 2025-09-08. Nested Optimal Transport Distances. https://arxiv.org/abs/2509.06702

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