# Pathwise Stochastic Control with Applications to Robust Filtering

## TL;DR

This paper introduces a pathwise stochastic control framework using rough differential equations to develop robust filters that handle parameter uncertainty, combining stochastic control and rough path theory.

## Contribution

It proposes a novel approach to pathwise stochastic control via rough differential equations and applies it to create robust filtering methods resilient to parameter uncertainty.

## Key findings

- Resolved degeneracy in control of noise coefficients.
- Developed robust filters using pathwise control and rough path theory.
- Demonstrated effectiveness in stochastic filtering applications.

## Abstract

We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the degeneracy phenomenon induced by directly controlling the coefficient of the noise term, and propose a simple procedure to resolve this degeneracy whilst retaining dynamic programming. As an application, we use pathwise stochastic control in the context of stochastic filtering to construct filters which are robust to parameter uncertainty, demonstrating an original application of rough path theory to statistics.