# General duality and dual attainment for adapted transport

arXiv: https://arxiv.org/abs/2401.11958 · HTML: https://mlsanity.com/paper/2401.11958/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2024.

## Built on by (most cited first, 2 of 2)

- [Neural Spacetimes for DAG Representation Learning](https://mlsanity.com/paper/2408.13885/) (2024)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)

## Abstract (arXiv)

We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, the causal and bicausal barycenter problem, and a multimarginal problem incorporating causality constraints. Moreover, we characterize polar sets in the causal and bicausal setting and discuss applications of our results in robust finance. We consider a non-dominated model of several financial markets where stocks are traded dynamically, but the joint stock dynamics are unknown. We show that a no-arbitrage assumption naturally leads to sets of multicausal couplings. Consequently, computing the robust superhedging price is equivalent to solving an adapted transport problem, and finding a superhedging strategy means solving the corresponding dual.