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 equ
ation. The existence and uniqueness of VNBSFE is established. The Pontryagin maximum principle is constructed for controlled NSFDE with Lagrange type cost functional.
In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an applicati
on, we discuss the optimal control of neutral stochastic functional differential equations, establish a Pontryagin maximum principle, and give an explicit optimal value for the linear optimal control.
