Infinite horizon optimal control problem of mean-field backward stochastic delay differential equation under partial information

This paper investigates an optimal control of an infinite horizon system governed by mean-field backward stochastic differential equation with delay and partial information. Firstly, we establish the existence and uniqueness results for a mean-field backward stochastic differential equation (BSDE) with average delay. Then a class of mean-field time-advanced stochastic differential equations (ASDEs) is introduced as the adjoint equations via duality relation. Meanwhile, necessary and sufficient conditions for optimal control under partial information on infinite horizon are derived. Finally, we apply the theoretical results to study linear-quadratic control problem on infinite horizon to obtain the optimal control, which is explicitly expressed by the solution of a mean-field forward-backward stochastic differential filtering equation.