Backward Anticipated Social Optima: Input Constraints and Partial Information

A class of stochastic linear-quadratic (LQ) dynamic optimization problems involving a large population is investigated in this work. Here, the agents cooperate with each other to minimize certain social costs. Furthermore, differently from the classic social optima literature, the dynamics in this framework are driven by anticipated backward stochastic differential equations (ABSDE) in which the terminal instead of the initial condition is specified and the anticipated terms are involved. The individual admissible controls are constrained in closed convex subsets , and the common noise is considered. As a result, the related social cost is represented by a recursive functional in which the initial state is involved. By virtue of the so-called anticipated person-by-person optimality principle , a decentralized strategy can be derived. This is based on a class of new consistency condition systems, which are mean-field-type anticipated forward-backward stochastic differential delay equations (AFBSDDEs). The well-posedness of such a consistency condition system is obtained through a discounting decoupling method. Finally, the corresponding asymptotic social optimality is proved.