LINEAR-QUADRATIC LARGE-POPULATION PROBLEM WITH PARTIAL INFORMATION: HAMILTONIAN APPROACH AND RICCATI APPROACH.

This paper studies a class of partial information linear-quadratic mean-field game problems. A general stochastic large population system is considered, where the diffusion term of the dynamic of each agent can depend on the state and control. We study both the control constrained case and the unconstrained case. In the control constrained case, by using a Hamiltonian approach and convex analysis, the explicit decentralized strategies can be obtained through a projection operator. The corresponding Hamiltonian type consistency condition system is derived, which turns out to be a nonlinear mean-field forward-backward stochastic differential equation with projection operator. The well-posedness of such equations is proved by using a discounting method. Moreover, the corresponding E-varepsilon -Nash equilibrium property is verified. In the control unconstrained case, the decentralized strategies can be further represented explicitly as the feedback of the filtered state through a Riccati approach. The existence and uniqueness of a solution to a new Riccati type consistency condition system is also discussed. As an application, a general interbank borrowing and lending problem is studied to illustrate that the effect of partial information cannot be ignored. [ABSTRACT FROM AUTHOR]