Abstract

Exit times of diffusion processes play an important role in the application of finance, insurance, biology, engineering, and so on. This article investigates the two-side exit time problems for the Vasicek model. By using Strong Markov property, the Laplace–Stieltjes transform (LST) of some exit times are obtained. And then the results are used to figure out the probability and mathematical expectation of the exit times. Finally, numerical examples are given to illustrate the applications of the LST of some exit times.

中文翻译：

---

Vasicek 模型两侧退出时间问题的精确解

摘要

扩散过程的退出时间在金融、保险、生物、工程等领域的应用中起着重要作用。本文研究 Vasicek 模型的两侧退出时间问题。利用强马尔可夫性质，得到了一些退出时间的拉普拉斯-斯蒂尔切斯变换（LST）。然后将结果用于计算退出时间的概率和数学期望。最后，给出数值例子来说明LST在一些退出时间的应用。