| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 76 | |
| Number of page(s) | 34 | |
| DOI | https://doi.org/10.1051/cocv/2024064 | |
| Published online | 07 October 2024 | |
Time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations
1
School of Mathematics, Sichuan University, Chengdu 610064, PR China
2
College of Mathematics and Physics, Chengdu University of Technology, Chengdu 610059, PR China
* Corresponding author: lu@scu.edu.cn
Received:
24
February
2024
Accepted:
19
August
2024
We study the time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research makes two contributions. Firstly, we introduce a novel type of Riccati equation system with parameters and constraint conditions, known as the generalized equilibrium Riccati equation. This equation system offers a comprehensive solution for the closedloop equilibrium strategy of the problem at hand. Secondly, we establish the well-posedness of the generalized equilibrium Riccati equation for the one-dimensional case, provided certain conditions are met.
Mathematics Subject Classification: 93E20 / 49N10
Key words: Stochastic linear quadratic control problem / forward–backward stochastic differential equation / time-inconsistency
© The authors. Published by EDP Sciences, SMAI 2024
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