调和分数Ornstein-Uhlenbeck金融模型的参数估计  

Parameter estimation of tempered fractional Ornstein-Uhlenbeck financial model

作　　者：王继霞[1] 王琳 李浩然 Wang Jixia;Wang Lin;Li Haoran(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China;Center for Economics,Finance and Management Studies,Hunan University,Changsha 410012,China)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007 [2]湖南大学经济管理研究中心,长沙410012

出　　处：《河南师范大学学报（自然科学版）》2025年第1期75-81,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11971154);河南省软科学研究计划项目(232400410034).

摘　　要：为了描述金融资产价格过程的长相依性和自相似性,首先构建由调和分数布朗运动驱动的分数Ornstein-Uhlenbeck(O-U)模型.由于调和分数布朗运动是分数布朗运动的推广,故所构建的模型具有更广泛的应用.然后基于离散观测样本,利用最小二乘方法,得到模型漂移参数的估计量,并证明了估计量的相合性和渐近分布.最后,通过模拟展示了所得估计量的有限样本性质,模拟结果显示估计量的值拟合参数真值的效果较好.In order to describe the long-range dependence and self-similarity of financial asset price process,this paper first constructs a fractional Ornstein-Uhlenbeck(O-U)model driven by tempered fractional Brownian motion.Because tempered fractional Brownian motion is a generalization of fractional Brownian motion,the model constructed has more extensive applications.Based on discrete observation samples,the estimator for the model of the drift parameter is obtained by using the least square method,the consistency of the estimator is proved,and the asymptotic distribution of the estimator is given.Finally,the simulation shows the finite sample property of the estimator,and the simulation results show that the estimator is effective.

关 键 词：最小二乘估计 调和分数布朗运动 ORNSTEIN-UHLENBECK过程 相合性 渐近分布 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]