Time-inconsistent Linear Quadratic Optimal Control Problem for Forward-Backward Stochastic Differential Equations
Optimization and Control
2023-12-15 v1
Abstract
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 closed-loop 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.
Cite
@article{arxiv.2312.08713,
title = {Time-inconsistent Linear Quadratic Optimal Control Problem for Forward-Backward Stochastic Differential Equations},
author = {Qi Lü and Bowen Ma},
journal= {arXiv preprint arXiv:2312.08713},
year = {2023}
}