平均场正倒向随机控制系统的最大值原理

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 143-155.

平均场正倒向随机控制系统的最大值原理

李瑞敬()

广东财经大学统计与数学学院广州 510320

收稿日期:2017-12-05 出版日期:2019-02-26 发布日期:2019-03-12
作者简介:李瑞敬, E-mail:li209981@sina.com
基金资助:
国家自然科学基金(11626063)

A General Maximum Principle for Forward-Backward Stochastic Control Systems of Mean-Field Type

Ruijing Li()

School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320

Received:2017-12-05 Online:2019-02-26 Published:2019-03-12
Supported by:
the NSFC(11626063)

摘要/Abstract

摘要：

该文研究具有时间不连续效用函数的平均场随机系统最优控制问题.其中，扩散项系数包含控制变量且控制区域非凸.借助于延拓的Ekeland变分原理及递归方法，建立平均场理论框架下一般形式的随机最大值原理.最后，求解一个线性二次问题以论证结果的可行性.

关键词: 平均场随机微分方程, 最大值原理, 伴随方程, 延拓的Ekeland变分原理

Abstract:

The present paper concerns with optimal control problems allowing for time inconsistent utility functions for instance of mean-field stochastic systems. Moreover, the control variable enters the diffusion coefficient and the control domain is non-convex. Via extended Ekeland's variational principle as well as the reduction method, a general stochastic maximum principle is established in the framework of mean-field theory. Finally, a linear-quadratic example is worked out to illustrate the application of the results.

Key words: Mean-field SDE, Maximum principle, Adjoint equation, Extended Ekeland's variational principle

中图分类号:

O110.64

李瑞敬. 平均场正倒向随机控制系统的最大值原理[J]. 数学物理学报, 2019, 39(1): 143-155.

Ruijing Li. A General Maximum Principle for Forward-Backward Stochastic Control Systems of Mean-Field Type[J]. Acta mathematica scientia,Series A, 2019, 39(1): 143-155.

参考文献 19

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