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Nested Optimal Transport Distances

Author

Listed:
  • 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.

Suggested Citation

  • Ruben Bontorno & Songyan Hou, 2025. "Nested Optimal Transport Distances," Papers 2509.06702, arXiv.org.
    • Handle: RePEc:arx:papers:2509.06702
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    References listed on IDEAS

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    1. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglbock & Manu Eder, 2019. "Adapted Wasserstein Distances and Stability in Mathematical Finance," Papers 1901.07450, arXiv.org, revised May 2020.
    2. Alois Pichler & Michael Weinhardt, 2022. "The nested Sinkhorn divergence to learn the nested distance," Computational Management Science, Springer, vol. 19(2), pages 269-293, June.
    3. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    4. Bion-Nadal, Jocelyne, 2009. "Time consistent dynamic risk processes," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 633-654, February.
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