Mathematics > Optimization and Control
[Submitted on 1 Mar 2025
]
Title: Linear-quadratic control for mean-field backward stochastic differential equations with random coefficients
Title: 带有随机系数的平均场倒向随机微分方程的线性二次控制
Abstract: 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).
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