MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL DELAYED EQUATIONS

被引：24

作者：

Huang, Jianhui ^{[1
]}

Shi, Jingtao ^{[2
]}

机构：

[1] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2012年 / 18卷 / 04期

基金：

中国博士后科学基金;

关键词：

Stochastic optimal control; maximum principle; stochastic differential delayed equation; anticipated backward differential equation; fully coupled forward-backward stochastic system; Clarke generalized gradient; LARGE INVESTOR; SYSTEMS;

D O I：

10.1051/cocv/2011204

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic control problems are discussed and both optimal controls are derived explicitly.

引用

页码：1073 / 1096

页数：24

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