Stochastic maximum principle of mean-field jump-diffusion systems with mixed delays (Q2242975)

Consider an optimal stochastic control problem having mean-field terms and random jumps, both pointwise, where moving-average delays of the state as well as the control can be incorporated. Applying the stochastic maximum principle, necessary and sufficient optimality conditions are derived. Two types of adjoint equations occur: The first consists of two coupled backward equations, where the first one is a mean-field anticipated backward stochastic differential equation (BSDE) with random jumps. The second adjoint equation consists also of two backward equations, where the first one, which is decoupled from the second one, is a mean-field time-advanced (BSDE) with random jumps. An application is considered.