Stochastic maximum principle for problems with delay with general dependence on the past

Understand

We prove a stochastic maximum principle for a control problem where the state equation is delayed both in the state and in the control, and also the final cost functional may depend on the past trajectories.

• The adjoint equations turn out to be a new form of linear anticipated backward stochastic differential equations (ABSDEs in the following), and we prove a direct formula to solve these equations.