Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1073-1096 |
| Number of pages | 24 |
| Journal | ESAIM - Control, Optimisation and Calculus of Variations |
| Volume | 18 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Oct 2012 |
Keywords
- Anticipated backward differential equation
- Clarke generalized gradient
- Fully coupled forward-backward stochastic system
- Maximum principle
- Stochastic differential delayed equation
- Stochastic optimal control
ASJC Scopus subject areas
- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics