| 刘臻.粘性解框架下的完全耦合正倒向随机系统 最优控制问题的验证定理[J].数学年刊A辑,2017,38(2):201~214 |
| 粘性解框架下的完全耦合正倒向随机系统 最优控制问题的验证定理 |
| A Verification Theorem for Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equations within the Framework of Viscosity Solutions |
| Received:March 27, 2015 Revised:December 01, 2015 |
| DOI：10.16205/j.cnki.cama.2017.0016 |
| 中文关键词: Stochastic optimal controls, Fully coupled forward-backwardstochastic differential equations, Verification theorem, Feedback controls |
| 英文关键词:Stochastic optimal controls, Fully coupled forward-backwardstochastic differential equations, Verification theorem, Feedback controls |
| 基金项目:本文受到国家自然科学基金(No.10325101,No.11171076)的资助. |
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| 中文摘要: |
| 研究了完全耦合正倒向随机控制系统的最优控制问题.
得到了粘性解框架下的, 控制变量同时出现在正倒向随机系统的漂移项和扩散项中的最优控制问题的验证定理.
还讨论了验证定理在构造随机最优反馈控制中的应用. |
| 英文摘要: |
| The optimal control of a fully coupled forward-backward
stochastic differential equations is considered where
control variables are allowed to enter into both drift
and diffusion terms. A verification theorem is proved
within the framework of viscosity solutions. The application of this verification theorem to the optimal
stochastic feedback controls is also discussed. |
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