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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (11): 50-57.doi: 10.6040/j.issn.1671-9352.0.2022.458

• • 上一篇    

含有乘性噪声的理性期望模型的最优控制

苌庆,亓庆源*,刘志强   

  1. 青岛大学自动化学院复杂性科学研究所, 山东 青岛 266071
  • 发布日期:2022-11-10
  • 作者简介:苌庆(1997— ),女,硕士研究生,研究方向为随机系统的优化控制. E-mail:changqingbp@163.com*通信作者简介:亓庆源(1990— ),男,博士,副教授,硕士生导师,研究方向为随机控制与最优估计. E-mail:qiqy123@163.com
  • 基金资助:
    国家自然科学基金资助项目(61903210);山东省自然科学基金资助项目(ZR2019BF002);中国博士后基金资助项目(2019M652324,2021T140354)

Optimal control of rational expectations model with multiplicative noise

CHANG Qing, QI Qing-yuan*, LIU Zhi-qiang   

  1. Institute of Complexity Science, School of Automation, Qingdao University, Qingdao 266071, Shandong, China
  • Published:2022-11-10

摘要: 研究了含有乘性噪声的理性预期模型的最优控制问题。用凸变分思想,建立了极大值原理,并给出了含乘性噪声的理性预期模型最优控制器存在的充分必要条件;通过解耦正倒向随机差分方程,给出了最优控制器的设计方法;并给出了数值例子来说明结果的有效性。

关键词: 理性预期模型, 乘性噪声, 极大值原理

Abstract: The optimal control of a rational expectations model with multiplicative noise is investigated. By using the convex variational method, the maximum principle is derived, and the necessary and sufficient solvability conditions are shown. By decoupling the forward and backward stochastic difference equations, the optimal control is derived. Finally, numerical example is given to show the effectiveness of the obtained results.

Key words: rational expectations model, multiplicative noise, maximum principle

中图分类号: 

  • O232
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