A general maximum principle for mean-field stochastic differential\n equations with jump processes

In this paper, we investigate the optimal control problems for stochastic\ndifferential equations (SDEs in short) of mean-field type with jump processes.\nThe control variable is allowed to enter into both diffusion and jump terms.\nThis stochastic maximum principle differs from the classical one in the sense\nthat here the first-order adjoint equation turns out to be a linear mean-field\nbackward SDE with jumps, while the second-order adjoint equation remains the\nsame as in Tang and Li's stochastic maximum principle [32]. Finally, for the\nreader's convenience we give some analysis results used in this paper in the\nAppendix.\n