First- and Second-Order Maximum Principles for Discrete-Time Stochastic Optimal Control With Recursive Utilities

• 成果类型: Article
• 署名作者: Song, Teng; Liu, Bin
• 署名单位: Wuhan University of Technology; Huazhong University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3261345
• 发表日期: 2024
• 页码: 43-54
• 关键词: Optimal control; Stochastic processes; mathematical models; COSTS; PROCESS CONTROL; Difference equations; Symmetric matrices; Adjoint equations; Discrete-time stochastic systems; recursive optimal control; stochastic maximum principle

摘要

This article deals with the discrete-time stochastic optimal control problems with recursive utilities under weakened convexity assumption. A new stochastic maximum principle is established. Moreover, by constructing two new adjoint equations and two new variational equations for the backward stochastic difference equation, we obtain the second-order necessary optimality condition of quasi-singular control. Finally, as an illustration, a discrete-time mean-variance portfolio selection mixed with a recursive utility functional optimization problem is solved.