  In this paper, we study an optimal control problem of a mean-field
forward-backward stochastic system with random jumps in progressive structure,
where both regular and singular controls are considered in our formula. In
virtue of the variational technology, the related stochastic maximum principle
(SMP) has been obtained, and it is essentially different from that in the
classical predictable structure. Specifically, there are three parts in our
SMP, i.e. continuous part, jump part and impulse part, and they are
respectively used to characterize the characteristics of the optimal controls
at continuous time, jump time and impulse time. This shows that the progressive
structure can more accurately describe the characteristics of the optimal
control at the jump time. We also give two linear-quadratic (LQ) examples to
show the significance of our results.
