# Stochastic control with rough paths

arXiv: https://arxiv.org/abs/1303.7160 · HTML: https://mlsanity.com/paper/1303.7160/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2013.

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

- [Dual Approaches to Stochastic Control via SPDEs and the Pathwise Hopf Formula](https://mlsanity.com/paper/2604.08155/) (2026)
- [Unified Optimality Conditions for Stochastic Optimal Control in the Rough Path and Ito Frameworks](https://mlsanity.com/paper/2609.38395/) (2026)

## Abstract (arXiv)

We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We propose a formulation based on rough paths and then obtain a generalization of Roger's duality formula [L. C. G. Rogers, 2007] from discrete to continuous time. We also make the link to old work of [Davis--Burstein, 1987].