# Pathwise stochastic control and a class of stochastic partial differential equations

arXiv: https://arxiv.org/abs/2301.09214 · HTML: https://mlsanity.com/paper/2301.09214/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [Pathwise Relaxed Optimal Control of Rough Differential Equations](https://mlsanity.com/paper/2402.17900/) (2024)

## Abstract (arXiv)

We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this equation, in the viscosity sense. Finally, we discuss a version of some corresponding stochastic pathwise Noether theorem.