论文标题
具有政权切换的受控条件平均FBSDE的全球最大原则
A Global Maximum Principle for Controlled Conditional Mean-field FBSDEs with Regime Switching
论文作者
论文摘要
本文专用于有条件的平均领域前向随机微分方程（简称FBSDES）的全局随机最大原理，并具有转换状态。控制域不必要地凸出，并且向后随机微分方程（简称BSDE）的驱动程序可能取决于$ z $。与非恢复效用的情况不同，一阶和二阶伴随方程都是高维线性BSDE。基于伴随方程式，我们揭示了一阶和二阶泰勒扩展的术语之间的关系。证明了一般的最大原则，该原则开发了Nguyen，Yin和Nguyen [22]的递归效用的工作。作为应用程序，考虑了线性季节问题，并研究了状态约束的问题。
This paper is devoted to a global stochastic maximum principle for conditional mean-field forward-backward stochastic differential equations (FBSDEs, for short) with regime switching. The control domain is unnecessarily convex and the driver of backward stochastic differential equations (BSDEs, for short) could depend on $Z$. Different from the case of non-recursive utility, the first-order and second-order adjoint equations are both high-dimensional linear BSDEs. Based on the adjoint equations, we reveal the relations among the terms of the first- and second-order Taylor's expansions. A general maximum principle is proved, which develops the work of Nguyen, Yin, and Nguyen [22] to recursive utility. As applications, the linear-quadratic problem is considered and a problem with state constraint is studied.
