Maximum principle for optimal control of neutral stochastic functional differential systems

This paper is concerned with optimal control of neutral stochastic functional differential equations (NSFDEs). The Pontryagin maximum principle is proved for optimal control, where the adjoint equation is a linear neutral backward stochastic functional equation of Volterra type (VNBSFE). The existence and uniqueness of the solution are proved for the general nonlinear VNBSFEs. Under the convexity assumption of the Hamiltonian function, a sufficient condition for the optimality is addressed as well.