# Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization

arXiv: https://arxiv.org/abs/1611.02610 · HTML: https://mlsanity.com/paper/1611.02610/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2016.

## Built on by (most cited first, 11 of 11)

- [Small Transformers Compute Universal Metric Embeddings](https://mlsanity.com/paper/2209.06788/) (2022)
- [Time-Causal VAE: Robust Financial Time Series Generator](https://mlsanity.com/paper/2411.02947/) (2024)
- [Neural Spacetimes for DAG Representation Learning](https://mlsanity.com/paper/2408.13885/) (2024)
- [Conditional COT-GAN for Video Prediction with Kernel Smoothing](https://mlsanity.com/paper/2106.05658/) (2021)
- [Unlocking optimal batch size schedules using continuous-time control and perturbation theory](https://mlsanity.com/paper/2312.01898/) (2023)
- [Fitted value iteration methods for bicausal optimal transport](https://mlsanity.com/paper/2306.12658/) (2023)
- [Distributionally robust risk evaluation with a causality constraint and structural information](https://mlsanity.com/paper/2203.10571/) (2022)
- [Auditing and Enforcing Conditional Fairness via Optimal Transport](https://mlsanity.com/paper/2410.14029/) (2024)
- [Nested Optimal Transport Distances](https://mlsanity.com/paper/2509.06702/) (2025)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)
- [PLOT: Progressive Localization via Optimal Transport in Neural Causal Abstraction](https://mlsanity.com/paper/2605.06979/) (2026)

## Abstract (arXiv)

The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal transport plans in the context of enlargement of filtrations, as the Kantorovich counterparts of the aforementioned non-adapted mappings. We provide a necessary and sufficient condition for a Brownian motion to remain a semimartingale in an enlarged filtration, in terms of certain minimization problems over sets of causal transport plans. The latter are also used in order to give robust transport-based estimates for the value of having additional information, as well as model sensitivity with respect to the reference measure, for the classical stochastic optimization problems of utility maximization and optimal stopping. Our results have natural extensions to the case of general multidimensional continuous semimartingales.