| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 35 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2023033 | |
| Published online | 24 May 2023 | |
Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems
1
Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, PR China
2
School of Mathematics, Shandong University, Jinan 250100, PR China
3
Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, PR China
† Corresponding author: wuzhen@sdu.edu.cn
Received:
29
July
2022
Accepted:
23
April
2023
This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and state processes are presented in the cost functional. Based on a Hilbert space method, necessary and sufficient conditions are derived for the solvability of the problem, and a general approach for constructing optimal controls is developed. The crucial step in this construction is to establish the solvability of a Riccati-type equation, which is accomplished under a fairly weak condition by investigating the connection with forward stochastic LQ optimal control problems.
Mathematics Subject Classification: 93E20 / 49N10 / 49N35 / 49K27
Key words: Indefinite / backward stochastic differential equation / linear-quadratic / optimal control / Riccati equation
This author is supported by NSFC grant 12271242, Guangdong Basic and Applied Basic Research Foundation 2021A1515010031, Shenzhen Fundamental Research General Program JCYJ20220530112814032, and National Key R&D Program of China 2022YFA1006102.
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.