Linear-Quadratic Optimal Control for Mean-Field Stochastic Differential Equations in Infinite-Horizon with Regime Switching

Fuente: arXiv
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Main Authors: Mei, Hongwei, Wei, Qingmeng, Yong, Jiongmin
Format: Preprint
Published: 2025
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author Mei, Hongwei
Wei, Qingmeng
Yong, Jiongmin
author_facet Mei, Hongwei
Wei, Qingmeng
Yong, Jiongmin
contents This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with conditional mean-field term in a switching regime environment. The orthogonal decomposition introduced in [21] has been adopted. Desired algebraic Riccati equations (AREs, for short) and a system of backward stochastic differential equations (BSDEs, for short) in infinite time horizon with the coefficients depending on the Markov chain have been derived. The determination of closed-loop optimal strategy follows from the solvability of ARE and BSDE. Moreover, the solvability of BSDEs leads to a characterization of open-loop solvability of the optimal control problem.
format Preprint
id arxiv_https___arxiv_org_abs_2501_00981
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Linear-Quadratic Optimal Control for Mean-Field Stochastic Differential Equations in Infinite-Horizon with Regime Switching
Mei, Hongwei
Wei, Qingmeng
Yong, Jiongmin
Optimization and Control
93E20, 49N10, 60F17
This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with conditional mean-field term in a switching regime environment. The orthogonal decomposition introduced in [21] has been adopted. Desired algebraic Riccati equations (AREs, for short) and a system of backward stochastic differential equations (BSDEs, for short) in infinite time horizon with the coefficients depending on the Markov chain have been derived. The determination of closed-loop optimal strategy follows from the solvability of ARE and BSDE. Moreover, the solvability of BSDEs leads to a characterization of open-loop solvability of the optimal control problem.
title Linear-Quadratic Optimal Control for Mean-Field Stochastic Differential Equations in Infinite-Horizon with Regime Switching
topic Optimization and Control
93E20, 49N10, 60F17
url https://arxiv.org/abs/2501.00981