The integral of geometric Brownian motion
The integral of geometric Brownian motion
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DOI：
10.1017/s0001867800010715
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发表时间：
2001-03-01
影响因子：
1.2
通讯作者：
Dufresne, D
中科院分区：
文献类型：
--
作者：
Dufresne, D
本文研究的是几何布朗运动在有限时间间隔内积分的概率定律。推导了倒积分定律的拉普拉斯变换的偏微分方程，并显示出分布密度的表达式。至少当布朗运动的归一化漂移是非负整数时，该表达式比之前获得的表达式具有一些优点。布格罗尔的恒等式以及布朗运动与相反漂移之间的关系也可以被视为这些结果的特例。
This paper is about the probability law of the integral of geometric Brownian motion over a finite time interval. A partial differential equation is derived for the Laplace transform of the law of the reciprocal integral, and is shown to yield an expression for the density of the distribution. This expression has some advantages over the ones obtained previously, at least when the normalized drift of the Brownian motion is a non-negative integer. Bougerol's identity and a relationship between Brownian motions with opposite drifts may also be seen to be special cases of these results.