论文标题
近似Barndorff-Nielsen和Shephard模型的首次退出时间分析，具有固定的自我分配差异过程
First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process
论文作者
论文摘要
在本文中，制定了Barndorff-Nielsen和Shephard模型的大约版本，该模型由Brownian Motion和LévySuportinator驱动。分析了该模型的日志返回过程的第一个外观时间。结果表明，有一定的概率，对数返回的第一范围时间过程可以分解为带有漂移的布朗运动的第一个退出时间的总和，以及带有漂移的Lévy下属的第一个退出时间。随后，研究了某些特定Lévy下属的第一个退出时间的概率密度函数，该时间连接到固定的，自我分解的方差过程。通过各种特殊功能，获得了三个这样的莱维下属概率时间的概率密度函数的分析表达式。结果已实施到经验指数S＆P 500数据集。
In this paper, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a Lévy subordinator, is formulated. The first-exit time of the log-return process for this model is analyzed. It is shown that with certain probability, the first-exit time process of the log-return is decomposable into the sum of the first exit time of the Brownian motion with drift, and the first exit time of a Lévy subordinator with drift. Subsequently, the probability density functions of the first exit time of some specific Lévy subordinators, connected to stationary, self-decomposable variance processes, are studied. Analytical expressions of the probability density function of the first-exit time of three such Lévy subordinators are obtained in terms of various special functions. The results are implemented to empirical S&P 500 dataset.
