离散观测下分数Vasicek模型的参数估计  

Parameter estimation for fractional Vasicek model with discrete observations

作　　者：程潘红 许志宏[3] Cheng Panhong;Xu Zhihong(Business School,University of Shanghai for Science and Technology,Shanghai 2000s,China;Institute of Mathematics and Finance,Chuzhou University,Chuzhou 239o,China;Public Teaching Department,Rizhao Polytechnic,Rizhao 276826,China)

机构地区：[1]上海理工大学管理学院,上海200093 [2]滁州学院数学与金融学院,安徽滁州239000 [3]日照职业技术学院公共教学部,山东日照276826

出　　处：《纯粹数学与应用数学》2022年第4期557-568,共12页Pure and Applied Mathematics

基　　金：安徽省高校自然科学重点研究项目(KJ2018A0429)。

摘　　要：分数Vasicek模型是对经典Vasicek随机利率模型的一种推广,它能够有效刻画利率序列的均值回复性和长记忆性.为将模型应用于实践,考虑离散观测下分数Vasicek模型中两个未知参数即长期均衡利率水平和短期利率偏离长期利率时的调节速度的估计问题.运用Borel-Cantelli引理、Markov不等式和Cauchy-Schwarz不等式,说明了未知参数估计量的强一致收敛性.The fractional Vasicek model is a generalization of the classical Vasicek stochastic interest rate model.It can effectively describe the mean reversion and long memory of interest rate series.In order to apply the model to practice,the estimation problem of unknown parameters,i.e.long-term equilibrium interest rate level and the adjustment speed when short-term interest rate deviates from long-term interest rate in the fractional Vasicek model with discrete observations is considered.By applying BorelCantelli lemma,Markov inequality and Cauchy Schwarz inequality,the strong consistency of the estimators are proved.

关 键 词：分数Vasicek模型 强一致性 离散观测 

分 类 号：O211.6[理学—概率论与数理统计]