Maximum Principle for Optimal Control of Neutral Stochastic Functional Differential Systems

TL;DR

This paper develops a maximum principle for optimal control of neutral stochastic functional differential systems, introducing a new class of backward stochastic equations and establishing their existence and uniqueness.

Contribution

It introduces neutral backward stochastic Volterra-type equations as adjoint equations and derives a Pontryagin maximum principle for controlled NSFDEs.

Findings

Existence and uniqueness of VNBSFEs proven

Maximum principle formulated for NSFDE control problems

New class of backward stochastic equations introduced

Abstract

In this paper, the optimal control problem of neutral stochastic functional differential equation (NSFDE) is discussed. A class of so-called neutral backward stochastic functional equations of Volterra type (VNBSFEs) are introduced as the adjoint equation. The existence and uniqueness of VNBSFE is established. The Pontryagin maximum principle is constructed for controlled NSFDE with Lagrange type cost functional.