Advances in Applied Probability

The integral of geometric Brownian motion

Daniel Dufresne

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
Adv. in Appl. Probab. Volume 33, Number 1 (2001), 223-241.

Dates
First available in Project Euclid: 30 August 2001

Permanent link to this document
http://projecteuclid.org/euclid.aap/999187905

Digital Object Identifier
doi:10.1239/aap/999187905

Mathematical Reviews number (MathSciNet)
MR2002c:60132

Zentralblatt MATH identifier
0980.60103

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 91B28

Keywords
Brownian motion Bougerol's identity Asian options

Citation

Dufresne, Daniel. The integral of geometric Brownian motion. Adv. in Appl. Probab. 33 (2001), no. 1, 223--241. doi:10.1239/aap/999187905. http://projecteuclid.org/euclid.aap/999187905.


Export citation