一类新的短记忆过程及其在金融中的应用  

A New Short Memory Process and Its Applications in Finance

作　　者：杨梓健 王晓天[1] YANG Zijian;WANG Xiaotian(School of Mathematics,South China University of Technology,Guangzhou,Guangdong 510640,China)

机构地区：[1]华南理工大学数学学院,广东广州510640

出　　处：《数学建模及其应用》2021年第2期17-24,共8页Mathematical Modeling and Its Applications

基　　金：国家自然科学基金(11071082,11271140)。

摘　　要：为了刻画风险资产的收益和波动率,提出一个新的非高斯过程E_(H)(t),该过程具有短记忆性和“高峰厚尾”的特性.此外,给出了该过程的基本性质,并且基于该过程构建了一个新的无套利股票价格模型.本文描绘该过程的样本路径和概率密度函数,对该过程的在险值进行模拟,并且与同方差的布朗运动作对比分析.结果表明,该过程比同方差的分数布朗运动更加高峰和更加厚尾.因此,基于该过程建立的模型更加符合实际金融市场的表现.In order to simulate the return and volatility of risky assets,a new non-Gaussian process is proposed,which has short memory,leptokurtosis and heavy tail distribution.In addition,the basic properties of the process is proposed,and a new non-arbitrage stock price model is constructed based on the process.In this paper,the sample path and probability density function of the process are described,and the value-at-risk of the process is simulated and compared with Brownian motion,which has the same variance as the process.The results show that the process has higher peak and heavier tail than the homovariance fractional Brownian motion.Therefore,the model based on this process is more consistent with the performance of the actual financial market.

关 键 词：次分数布朗运动 高峰厚尾 短记忆性 无套利机会 

分 类 号：O29[理学—应用数学]