Necessary Conditions for Optimal Control of SPDE with locally monotone coefficients

TL;DR

This paper establishes necessary optimality conditions for controlling SPDEs with locally monotone coefficients using a maximum principle derived through backward stochastic PDEs.

Contribution

It introduces a maximum principle for SPDE control problems with locally monotone coefficients, expanding the theoretical framework for stochastic optimal control.

Findings

Derived a maximum principle for SPDEs with locally monotone coefficients

Established necessary conditions for optimal control in this setting

Utilized adjoint backward SPDEs to obtain the results

Abstract

The aim of this paper is to derive a maximum principle for a control problem governed by a stochastic partial differential equation (SPDE) with locally monotone coefficients. In particular, necessary conditions for optimality for this stochastic optimal control problem are obtained by using the adjoint backward stochastic partial differential equation (BSPDE).