论不确定微分方程的加权阈矩估计及其在银行间利率分析中的应用

3区 计算机科学 Q1 Computer Science Journal of Ambient Intelligence and Humanized Computing Pub Date : 2024-07-12 DOI:10.1007/s12652-024-04828-5
Jiajia Wang, Helin Gong, Anshui Li
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引用次数: 0

摘要

不确定性理论是建立信念度模型的数学分支。在不确定性理论的框架内,不确定变量用来表示具有不确定性的量,不确定过程用来模拟不确定量的演化过程。不确定微分方程是一种涉及不确定过程的微分方程,已成功应用于金融、最优控制、微分博弈、流行病传播等诸多学科。不确定微分方程已成为处理动态不确定系统的主要工具。不确定微分方程研究的关键问题之一是根据观测数据估计相关参数。然而,在事先不知道方程中相应项的结构时,解决这个问题相对困难。为了解决这个问题,本文提出了一种非参数估计技术,称为同质不确定微分方程的加权阈值矩估计。本文通过对中国上海银行间同业拆放利率的实证研究,举例说明了我们的方法的可行性和效率。本文最后提出了结束语和未来研究建议。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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On weighted threshold moment estimation of uncertain differential equations with applications in interbank rates analysis

Uncertainty theory is a branch of mathematics for modeling belief degrees. Within the framework of uncertainty theory, uncertain variable is used to represent quantities with uncertainty, and uncertain process is used to model the evolution of uncertain quantities. Uncertain differential equation is a type of differential equation involving uncertain processes, which has been successfully applied in many disciplines such as finance, optimal control, differential game, epidemic spread and so on. Uncertain differential equation has become the main tool to deal with dynamic uncertain systems. One of the key issues within the research of uncertain differential equations is the estimation of parameters involved based on the observed data. However, it is relatively difficult to solve this issue when the structures of the corresponding terms in the equations are not known in advance. To address this problem, one nonparametric estimation technique called weighted threshold moment estimation for homogeneous uncertain differential equations is proposed in this paper when no prior information about the terms is obtained. Numerical examples are presented to demonstrate the feasibility and efficiency of our method, highlighted by an empirical study of the Shanghai Interbank Offered Rate in China. The paper concludes with final remarks and recommendations for future research.

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来源期刊
Journal of Ambient Intelligence and Humanized Computing
Journal of Ambient Intelligence and Humanized Computing COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCEC-COMPUTER SCIENCE, INFORMATION SYSTEMS
CiteScore
9.60
自引率
0.00%
发文量
854
期刊介绍: The purpose of JAIHC is to provide a high profile, leading edge forum for academics, industrial professionals, educators and policy makers involved in the field to contribute, to disseminate the most innovative researches and developments of all aspects of ambient intelligence and humanized computing, such as intelligent/smart objects, environments/spaces, and systems. The journal discusses various technical, safety, personal, social, physical, political, artistic and economic issues. The research topics covered by the journal are (but not limited to): Pervasive/Ubiquitous Computing and Applications Cognitive wireless sensor network Embedded Systems and Software Mobile Computing and Wireless Communications Next Generation Multimedia Systems Security, Privacy and Trust Service and Semantic Computing Advanced Networking Architectures Dependable, Reliable and Autonomic Computing Embedded Smart Agents Context awareness, social sensing and inference Multi modal interaction design Ergonomics and product prototyping Intelligent and self-organizing transportation networks & services Healthcare Systems Virtual Humans & Virtual Worlds Wearables sensors and actuators
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