This paper investigates the hitting time problems of sticky Brownian motion and their applications in optimal stopping and bond pricing. We study the Laplace transform of first hitting time over the constant and random jump boundary, respectively. The results about hitting the constant boundary serve for solving the optimal stopping problem of sticky Brownian motion. By introducing the sharpo ratio, we settle the bond pricing problem under sticky Brownian motion as well. An interesting result shows that the sticky point is in the continuation region and all the results we get are in closed form.

中文翻译：

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粘性布朗运动的击中时间问题及其在最优停止和债券定价中的应用

本文研究了粘性布朗运动的打击时间问题及其在最优停止和债券定价中的应用。我们分别研究了恒定和随机跳跃边界上的第一次击球时间的拉普拉斯变换。达到恒定边界的结果有助于解决粘性布朗运动的最优停止问题。通过引入夏普比率，我们也解决了粘性布朗运动下的债券定价问题。一个有趣的结果表明，粘性点在延续区域，我们得到的所有结果都是封闭的。