数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (2): 437-449.doi: 10.1007/s10473-021-0208-z

• 论文 • 上一篇    下一篇

MAXIMUM PRINCIPLE FOR STOCHASTIC OPTIMAL CONTROL PROBLEM WITH DISTRIBUTED DELAYS

张启侠   

  1. School of Mathematical Sciences, University of Jinan, Jinan 250022, China
  • 收稿日期:2019-11-29 修回日期:2020-08-27 出版日期:2021-04-25 发布日期:2021-04-29
  • 作者简介:Qixia ZHANG,E-mail:zhangqixia110@163.com
  • 基金资助:
    The author is supported by the National Natural Science Foundation of China (11701214) and Shandong Provincial Natural Science Foundation, China (ZR2019MA045).

MAXIMUM PRINCIPLE FOR STOCHASTIC OPTIMAL CONTROL PROBLEM WITH DISTRIBUTED DELAYS

Qixia ZHANG   

  1. School of Mathematical Sciences, University of Jinan, Jinan 250022, China
  • Received:2019-11-29 Revised:2020-08-27 Online:2021-04-25 Published:2021-04-29
  • About author:Qixia ZHANG,E-mail:zhangqixia110@163.com
  • Supported by:
    The author is supported by the National Natural Science Foundation of China (11701214) and Shandong Provincial Natural Science Foundation, China (ZR2019MA045).

摘要: This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, we establish a necessary maximum principle and a sufficient verification theorem. In particular, we deal with the controlled stochastic system where the distributed delays enter both the state and the control. To explain the theoretical results, we apply them to a dynamic advertising problem.

关键词: Distributed delay, generalized anticipated backward stochastic differential equations, optimal control, maximum principle

Abstract: This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, we establish a necessary maximum principle and a sufficient verification theorem. In particular, we deal with the controlled stochastic system where the distributed delays enter both the state and the control. To explain the theoretical results, we apply them to a dynamic advertising problem.

Key words: Distributed delay, generalized anticipated backward stochastic differential equations, optimal control, maximum principle

中图分类号: 

  • 93E20