Volume 29, 2023
|Number of page(s)||30|
|Published online||24 May 2023|
Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems
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: email@example.com
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.
This author is supported by NSFC grants 11831010 and 61961160732, Shandong Provincial Natural Science Foundation ZR2019ZD42, and the Taishan Scholars Climbing Program of Shandong (TSPD20210302).
© 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.
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