一类带Poisson跳的延迟利率波动率模型数值解的收敛性

doi:10.13438/j.cnki.jdzk.2025.05.003

吉首大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (5): 10-18.DOI: 10.13438/j.cnki.jdzk.2025.05.003

一类带Poisson跳的延迟利率波动率模型数值解的收敛性

冯登宏，李志民

（安徽工程大学数理与金融学院，安徽芜湖 241000）

出版日期:2025-09-25 发布日期:2025-11-07
作者简介:冯登宏（1999—），男，安徽六安人，安徽工程大学数理与金融学院硕士研究生，主要从事金融数学研究
基金资助:
国家自然科学基金面上资助项目（61873294）；安徽高校省级自然科学研究重大项目(KJ2019ZD16)

Convergence Analysis of Numerical Solution of Delayed Interest Rate Model with Poisson Jumps

FENG Denghong,LI Zhimin

(School of Mathematics,Physics and Finance,Anhui Polytechnic University,Wuhu 241000,Anhui China)

Online:2025-09-25 Published:2025-11-07

摘要/Abstract

摘要：构造了带延迟利率波动率和Poisson跳的Ait-Sahalia模型,并引入改进截断Euler-Maruyama(EM)法探究其动态特性.在局部Lipschitz条件和Khasminskii-型条件的理论框架下，证明了模型的改进截断EM法的数值解能够强收敛到模型的真实解.

关键词： 延迟利率波动率, 改进截断Euler-Maruyama法, Ait-Sahalia模型, Poisson跳

Abstract: An Ait-Sahalia interest rate model is constructed with delayed volatility driven by Poisson jumps,and its dynamic properties are investigated through a modified truncated Euler-Maruyama (EM) method.Under the theoretical framework of local Lipschitz conditions and Khasminskii-type conditions,it is proved that the numerical solution generated by the modified truncated EM method converges strongly to the true solution of the model.

Key words: delayed interest volatility, modified truncated Euler-Maruyama scheme, Ait-Sahalia, Poisson jumps

冯登宏, 李志民. 一类带Poisson跳的延迟利率波动率模型数值解的收敛性[J]. 吉首大学学报（自然科学版）, 2025, 46(5): 10-18.

FENG Denghong, LI Zhimin. Convergence Analysis of Numerical Solution of Delayed Interest Rate Model with Poisson Jumps[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(5): 10-18.

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一类带Poisson跳的延迟利率波动率模型数值解的收敛性

Convergence Analysis of Numerical Solution of Delayed Interest Rate Model with Poisson Jumps

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