论文标题
由MFSDE管理的最佳控制问题具有多默认
Optimal Control Problems Governed by MFSDEs with multi-defaults
论文作者
论文摘要
在本文中，我们解决了一个最佳控制问题，该问题由具有多个默认值（MMFSDES）的平均场随机微分方程系统控制。我们将全局最佳控制问题转换为几个由单个默认值（SMFSDES）的均值场随机微分方程系统控制的最佳控制子问题，并得出了这些子问题的足够和必要的最大原理。我们还分别为MMFSDE和具有多个默认值（MMFBSDES）的均值向后随机微分方程提供了解决方案的存在和唯一性。最后，作为一个例子，我们的结果被应用于获得最佳控制问题的明确解决方案，其成本函数被视为具有多个默认值的递归实用程序。
In this paper, we solve an optimal control problem governed by a system of mean-field stochastic differential equations with multiple defaults (MMFSDEs). We transform the global optimal control problem into several optimal control subproblems governed by a system of mean-field stochastic differential equations with single default (SMFSDEs) and derive both the sufficient and necessary maximum principles for these subproblems. We also give the existence and uniqueness of solutions to the MMFSDEs and the mean-field backward stochastic differential equations with multiple defaults (MMFBSDEs), respectively. Finally, as an example, our results are applied to obtain the explicit solution for an optimal control problem whose cost function is considered as a recursive utility process with multiple defaults.
