2024/01/15 by Yuhang Li, Li, Yuhang, Yuecai Han +1
Economics, Econometrics and Finance · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2401.07520
openalex publication_date 2024/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and uniqueness of the solution of this equation. We obtain the stochastic maximum principle of the control system with time-varying delay by introducing a kind of generalized anticipated backward stochastic differential equations. We prove the existence and uniqueness of the solution of this adjoint equation. As an application, the linear quadratic moving average control problem is investigated to illustrate the main result.