# Nested Optimal Transport Distances

arXiv: https://arxiv.org/abs/2509.06702 · HTML: https://mlsanity.com/paper/2509.06702/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Causal transport in discrete time and applications](https://mlsanity.com/paper/1606.04062/) (2016)
- [Computational methods for adapted optimal transport](https://mlsanity.com/paper/2203.05005/) (2022)
- [Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization](https://mlsanity.com/paper/1611.02610/) (2016)
- [Time-Causal VAE: Robust Financial Time Series Generator](https://mlsanity.com/paper/2411.02947/) (2024)
- [Deep Generative Modeling for Financial Time Series with Application in VaR: A Comparative Review](https://mlsanity.com/paper/2401.10370/) (2024)
- [Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance](https://mlsanity.com/paper/2501.03993/) (2025)
- [Fitted value iteration methods for bicausal optimal transport](https://mlsanity.com/paper/2306.12658/) (2023)
- [Entropic adapted Wasserstein distance on Gaussians](https://mlsanity.com/paper/2412.18794/) (2024)

## Abstract (arXiv)

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.