Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs  

作　　者：Qi Lü Bowen Ma 

机构地区：[1]School of Mathematics,Sichuan University,Chengdu 610064,China

出　　处：《Science China Mathematics》2024年第1期211-236,共26页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.12025105, 11971334 and 11931011);the Chang Jiang Scholars Program and the Science Development Project of Sichuan University (Grant Nos. 2020SCUNL101 and 2020SCUNL201)。

摘　　要：A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).

关 键 词：linear-quadratic optimal control problem time-inconsistent cost functional generalized Riccati equation indefinite control weight cost closed-loop equilibrium strategy 

分 类 号：O231[理学—运筹学与控制论]