Linear-quadratic control for mean-field backward stochastic differential equations with random coefficients

Fuente: arXiv
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Main Authors: Xiong, Jie, Xu, Wen, Yang, Ying
Format: Preprint
Published: 2025
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author Xiong, Jie
Xu, Wen
Yang, Ying
author_facet Xiong, Jie
Xu, Wen
Yang, Ying
contents In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique solvability of the optimality system for this control problem through the variational method. Subsequently, we reformulate the mean-field linear-quadratic (MF-BSLQ) problem as a constrained BSDE control problem by imposing constraints on the expectation processes, which we solve using the Extended Lagrange multiplier method. Finally, we derive an explicit expression for the optimal control associated with Problem (MF-BSLQ).
format Preprint
id arxiv_https___arxiv_org_abs_2503_00369
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Linear-quadratic control for mean-field backward stochastic differential equations with random coefficients
Xiong, Jie
Xu, Wen
Yang, Ying
Optimization and Control
In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique solvability of the optimality system for this control problem through the variational method. Subsequently, we reformulate the mean-field linear-quadratic (MF-BSLQ) problem as a constrained BSDE control problem by imposing constraints on the expectation processes, which we solve using the Extended Lagrange multiplier method. Finally, we derive an explicit expression for the optimal control associated with Problem (MF-BSLQ).
title Linear-quadratic control for mean-field backward stochastic differential equations with random coefficients
topic Optimization and Control
url https://arxiv.org/abs/2503.00369