Time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations

被引：0
|
作者：
Lue, Qi [1 ]
Ma, Bowen [2 ]
机构：
[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China
[2] Chengdu Univ Technol, Coll Math & Phys, Chengdu 610059, Peoples R China
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2024年 / 30卷
关键词：
Stochastic linear quadratic control problem; forward-backward stochastic differential equation; time-inconsistency; PRINCIPLE;
D O I：
10.1051/cocv/2024064
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
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页数：34
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