Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups
Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups
复制标题
停止扩散过程的公式，其停止时间基于回撤和回撤
DOI：
10.1016/j.spa.2009.01.002
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发表时间：
2009
影响因子：
1.4
通讯作者：
O. Hadjiliadis
中科院分区：
文献类型：
--
作者：
L. Pospisil;J. Vecer;O. Hadjiliadis
本文研究了一般扩散模式中的水位下降过程和水位上升过程。主要的结果是一个公式的联合分布的运行最小值和运行最大值的过程中停止的时间的第一滴的大小a。因此，我们得到了规模a的缩减先于规模B的缩减的概率，反之亦然。结果被应用到几个例子的扩散过程，如漂移布朗运动，Ornstein-Uhlenbeck过程，和Cox-Ingersoll-Ross过程。
This paper studies drawdown and drawup processes in a general diffusion model. The main result is a formula for the joint distribution of the running minimum and the running maximum of the process stopped at the time of the first drop of size a. As a consequence, we obtain the probabilities that a drawdown of size a precedes a drawup of size b and vice versa. The results are applied to several examples of diffusion processes, such as drifted Brownian motion, Ornstein–Uhlenbeck process, and Cox–Ingersoll–Ross process.