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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]

We consider a class of linear-quadratic-Gaussian mean-field games having a major agent and numerous heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets Γk of Rm. The decentralized strategies of individual agents and the consistency condition system are represented in a unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on Γk . The well-posedness of the consistency system is established in both the local and global cases through the contraction mapping and discounting methods, respectively. A related ε -Nash-equilibrium property is also verified. [ABSTRACT FROM AUTHOR]

This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum principle and the dynamic programming principle for such a control problem without the assumption that the value is smooth enough; the set inclusions among the sub- and super-jets of the value function and the first-order and secondorder adjoint processes as well as the generalized Hamiltonian function are established. Moreover, by comparing these results with the classical ones in Yong and Zhou [Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999], it is natural to obtain the first- and second-order adjoint equations of Hu [Probability, Uncertainty and Quantitative Risk, 2 (2017), 1]. [ABSTRACT FROM AUTHOR]

We consider a kind of stochastic exit time optimal control problem in which the cost functional is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control problem. Then, extending Peng's backward semigroup method, we show the dynamic programming principle. Moreover, we prove that the value function is a viscosity solution to the following generalized Hamilton{Jacobi{Bellman equation with Dirichlet boundary condition: inf vϵV {L(x; v)u(x) + f(x; u(x)∇u(x)σ(x; v); v)} = 0, x ϵ D and u(x) = g(x), x ϵ δD where D is a bounded set in ℝd, V is a compact set in ℝk and for u ϵ C2(D) and (x; v) ϵ D × V L(x; v)u(x): 1/2 Σdi, j=1 (σσ)* i,j (x,v) δ2u/δxiδxj (x) + Σdi=1 bi (x; v) δu/δxi(x). [ABSTRACT FROM AUTHOR]