We consider a stochastic optimal control problem of a forward-backward system in which the
control variable consists of two components: the continuous control and the impulse control.
The domain of the control is assumed to be convex. Necessary optimality conditions of the
Pontryagin maximum principle type are obtained for this stochastic optimal control problem.
We also give additional conditions, under which the necessary optimality conditions turn out
to be sufficient.

This paper is concerned with the optimal control problems of forward-backward delay
systems involving impulse controls. The authors establish a stochastic maximum principle
for this kind of systems. The most distinguishing features of the proposed problem are that
the control variables consist of regular and impulsive controls, both with time delay, and that
the domain of regular control is not necessarily convex. The authors obtain the necessary
and sufficient conditions for optimal controls, which have potential applications in …