| 含有乘性噪声的理性期望模型的最优控制 |
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| 引用本文： | 苌庆,亓庆源,刘志强.含有乘性噪声的理性期望模型的最优控制[J].山东大学学报(理学版),2022,57(11):50-57. |
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| 作者姓名： | 苌庆 亓庆源 刘志强 |
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| 作者单位： | 青岛大学自动化学院复杂性科学研究所, 山东 青岛 266071 |
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| 基金项目： | 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) |
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| 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。
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| 关 键 词： | 理性预期模型 乘性噪声 极大值原理 |
Optimal control of rational expectations model with multiplicative noise |
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| CHANG Qing,QI Qing-yuan,LIU Zhi-qiang.Optimal control of rational expectations model with multiplicative noise[J].Journal of Shandong University,2022,57(11):50-57. |
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| Authors: | CHANG Qing QI Qing-yuan LIU Zhi-qiang |
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| Institution: | Institute of Complexity Science, School of Automation, Qingdao University, Qingdao 266071, Shandong, China |
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| 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. |
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| Keywords: | rational expectations model multiplicative noise maximum principle |
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