论文标题
线性季度大量人口问题与部分信息：哈密顿量方法和riccati方法
Linear-Quadratic Large-Population Problem with Partial Information: Hamiltonian Approach and Riccati Approach
论文作者
论文摘要
本文研究了一类部分信息线性二次平均场游戏问题。考虑了一般的随机大种群系统，其中每个代理的动态的扩散项可以取决于状态和控制。我们研究了对照限制的病例和不受约束的情况。在控制约束的情况下，通过使用哈密顿量方法和凸分析，可以通过投影操作员获得明确的分散策略。得出了相应的汉密尔顿类型一致性条件系统，事实证明，它是带有投影算子的非线性平均前面前向随机微分方程。通过使用折现方法证明了这种方程式的适合性。此外，还验证了相应的$ \ varepsilon $ -NASH平衡属性。在控制不受约束的情况下，可以通过Riccati方法明确表示分散的策略作为过滤状态的反馈。还讨论了对新的Riccati类型一致性条件系统的解决方案的存在和唯一性。作为一种应用程序，研究了一般的银行间借贷和贷款问题，以说明不忽略部分信息的效果。
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 unconstrained case. In control constrained case, by using Hamiltonian approach and convex analysis, the explicit decentralized strategies can be obtained through 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 kind of equations is proved by using discounting method. Moreover, the corresponding $\varepsilon$-Nash equilibrium property is verified. In control unconstrained case, the decentralized strategies can be further represented explicitly as the feedback of filtered state through 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 inter-bank borrowing and lending problem is studied to illustrate that the effect of partial information cannot be ignored.
