Duality methods in stochastic optimal control

TL;DR

This paper establishes two duality frameworks for the value function in stochastic optimal control problems, including cases with controlled diffusion, thus extending existing theoretical understanding.

Contribution

It introduces duality descriptions applicable to controlled diffusion problems, filling a gap in the current literature.

Findings

Duality descriptions for the value function are proven.

The results extend to controlled diffusion cases.

The paper advances theoretical foundations of stochastic control.

Abstract

We prove two duality descriptions of the value function for a generic stochastic optimal problem. These descriptions also hold when the diffusion is controlled, a case left open by the literature so far.