| Issue |
ESAIM: COCV
Volume 18, Number 4, October-December 2012
|
|
|---|---|---|
| Page(s) | 1073 - 1096 | |
| DOI | https://doi.org/10.1051/cocv/2011204 | |
| Published online | 16 January 2012 | |
Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations∗
1
Department of Applied Mathematics, The Hong Kong Polytechnic
University, Hung Hom,
Kowloon, Hong Kong,
P.R. China
majhuang@inet.polyu.edu.hk
2
School of Mathematics, Shandong University,
Jinan
250100, P.R.
China
shijingtao@sdu.edu.cn
Received:
12
August
2010
Revised:
13
August
2011
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.
Mathematics Subject Classification: 93E20 / 60H10 / 34K50
Key words: Stochastic optimal control / maximum principle / stochastic differential delayed equation / anticipated backward differential equation / fully coupled forward-backward stochastic system / Clarke generalized gradient
Jianhui Huang was supported by Departmental General Research Fund (No. A-SA69) and RGC Earmarked Grants of The Hong Kong Polytechnic University (Nos. 500909, 501010). Jingtao Shi was supported by China Postdoctoral Science Foundation Funded Project (No. 20100481278), Postdoctoral Innovation Foundation Funded Project of Shandong Province (No. 201002026), National Natural Sciences Foundations of China (No. 11126209) and Shandong Province (No. ZR2011AQ012), Research Award Fund for Outstanding Young and Middle-aged Scientists of Shandong Province (No. BS2011SF010), and Independent Innovation Foundation of Shandong University (IIFSDU, No. 2010TS060).
© EDP Sciences, SMAI, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.