A general maximum principle for partially observed mean-field stochastic system with random jumps in progressive structure

We study the progressive optimal control for partially observed stochastic system of mean-field type with random jumps. The cost function and the observation are also of mean-field type. The control is allowed to enter the diffusion, jump coefficient and the observation. The control domain need not be convex. We obtain the maximum principle for the partially observable progressive optimal control by a special spike variation. The maximum principle in the progressive structure is different from the classical case.