论文标题
在统治单调性条件和LQ问题的应用下，平均场型FBSDE
Mean-Field Type FBSDEs under Domination-Monotonicity Conditions and Application to LQ Problems
论文作者
论文摘要
本文涉及一类平均型号类型的耦合向前的随机微分方程（简称MF-FBSDE），其中耦合以整体术语，终端项和初始项以整体术语出现。受到各种均值线性季节（MF-LQ，对于简短）最佳控制问题的启发，我们提出了一种随机的统治单调性条件，在该条件下，在该条件下，我们在该条件下和通常的Lipschitz条件上获得了良好的态度，因此对MF-FBSD的态度良好，在正方形的含义上对MF-FBSD产生了相关性的依赖性和相关依赖性的依赖性的依赖性，并具有相关性的依赖性，并且是相关的依赖性的依赖性。 MF-FBSDE依次将文献中的MF-LQ问题扩展到一般情况，在这种情况下，初始状态或终端状态也同时受到控制，并给出相关独特的最佳控制的明确表达。
This paper is concerned with a class of mean-field type coupled forward-backward stochastic differential equations (MF-FBSDEs, for short), in which the coupling appears in integral terms, terminal terms, and initial terms. Inspired by various mean-field type linear-quadratic (MF-LQ,for short) optimal control problems, we proposed a type of randomized domination-monotonicity conditions, under which and the usual Lipschitz condition, we obtain a well-posedness result on MF-FBSDEs in the sense of square integrability including the unique solvability, an estimate of the solution, and the related continuous dependence property of the solution on the coefficients.The result of MF-FBSDEs in turn extends MF-LQ problems in the literature to a general situation where the initial states or the terminal states are also controlled at the same time, and gives explicit expressions of the related unique optimal controls.
