Stochastic maximum principle for a generalized volterra control system

In this paper, we study the stochastic optimal control problem for a generalized Volterra control system. The corresponding state process is a class of generalized stochastic Volterra integral-differential equations. We prove the existence and uniqueness of the solution of this type of equations. We derive the stochastic maximum principle for the optimal control system by introducing a class of generalized anticipated backward stochastic differential equations as the adjoint equation. We establish the existence and uniqueness of solutions to this adjoint equation. As an application, the linear quadratic Volterra control problem is investigated to illustrate the main results.