Stochastic optimal control for backward stochastic partial differential systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Meng, Qingxin^1,2  Shi, Peng^3,4 

[1] Huzhou Univ, Dept Math Sci, Huzhou 313000, Zhejiang, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Victoria Univ, Sch Sci & Engn, Melbourne, Vic 8001, Australia

[4] Univ Adelaide, Sch Elect & Elect Engn, Adelaide, SA 5005, Australia

关键词: Backward stochastic partial differential equation;    Stochastic maximum principle;    Stochastic evolution equation;    Backward stochastic evolution equation;    Verification theorem;   

DOI  :  10.1016/j.jmaa.2013.01.053

来源: Elsevier

【 摘 要 】

This paper studies optimal controls for a class of backward stochastic partial differential systems in the abstract evolution form. Under the assumption of a convex control domain, necessary and sufficient conditions for an admissible control to be optimal are derived in the form of stochastic maximum principles by means of a convex variation method and a duality technique. As an application, the optimal control for a linear backward stochastic evolution equation (BSEE) with quadratic cost criteria (called BSEELQ problem) is discussed, and the corresponding optimal control is characterized via the stochastic Hamilton system which is a linear full-coupled forward backward stochastic evolution equation (FBSEE) and consists of the state equation, the adjoint equation and the dual presentation of the optimal control. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free