Stochastic optimal control for backward stochastic partial differential systems

Qingxin Meng*, Peng Shi

*Corresponding author for this work

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)758-771
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume402
Issue number2
DOIs
Publication statusPublished - 15 Jun 2013
Externally publishedYes

Keywords

  • backward stochastic evolution equation
  • backward stochastic partial differential equation
  • stochastic evolution equation
  • stochastic maximum principle
  • verification theorem

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