带跳和马尔科夫转换随机利率模型长时间行为  

Long-term Behavior of Stochastic Interest Rate Models with Jumps and Markov Switching

作　　者：许自莉 李曼曼[1] XU Zili;LI Manman(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《山西大学学报（自然科学版）》2023年第2期309-320,共12页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12001068)。

摘　　要：考虑利率的波动性、随机性和资产价格的不连续性,本文通过建立带泊松跳跃和马尔科夫转换的CIR模型,研究瞬时利率的长时间行为。利用遍历理论和Lyapunov函数,证明随机利率过程存在唯一的平稳分布。而且,由于参数都服从马尔科夫过程,带跳和马尔科夫转换过程中的长时间利率行为的收敛性,与马尔科夫链的转移概率和随机扰动项系数密切相关。Considering the volatility and randomness of interest rate and the discontinuity of asset price,this paper studies the longterm behavior of instantaneous interest rate by establishing CIR model with Poisson jumps and Markov switching.Using ergodic theory and Lyapunov function,it is proved that the stochastic interest rate process has a unique stationary distribution.Moreover,since all the parameters are subject to Markov process,the convergence of the long-time interest rate behavior in the process of band jumps and Markov switching is closely related to the transfer probability of Markov chain and the random perturbation term coefficient.

关 键 词：随机微分方程 CIR模型 马尔科夫转换 平稳分布 

分 类 号：O211.63[理学—概率论与数理统计]