Necessary and sufficient conditions of optimal control for infinite dimensional SDEs

TL;DR

This paper establishes a comprehensive maximum principle for optimal control of infinite-dimensional stochastic differential equations driven by martingales, applicable even with non-convex control domains, using adjoint backward SDEs.

Contribution

It provides necessary and sufficient conditions for optimality in infinite-dimensional stochastic control problems with non-convex control domains.

Findings

Derived a general maximum principle for infinite-dimensional SDEs.

Extended the principle to non-convex control domains.

Utilized adjoint backward SDEs for the analysis.

Abstract

A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes its values in a separable Hilbert space and the control domain need not be convex. The result is obtained by using the adjoint backward stochastic differential equation.