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

A maximum principle for progressive optimal control of mean-filed forward-backward stochastic system involving random jumps and impulse controls