Mathematics – Probability
Scientific paper
2002-05-07
Mathematics
Probability
18 pages, 2 figures
Scientific paper
This paper studies the law of any power of the integral of geometric Brownian motion over any finite time interval. As its main results, two integral representations for this law are derived. This is by enhancing the Laplace transform ansatz of Yor (1992) with complex analytic methods, which is the main methodological contribution of the paper. The one of our integrals has a similar structure to that obtained by Yor, while the other is in terms of Hermite functions as those of Dufresne (2001). Performing or not performing a certain Girsanov transformation is identified as the source of these two forms of the laws. While our results specialize for exponents equal to 1 to those obtained by Yor, they yield on specialization representations for the exponent equal to minus 1 laws which are markedly different from those obtained by Dufresne.
No associations
LandOfFree
On the integral of geometric Brownian motion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the integral of geometric Brownian motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the integral of geometric Brownian motion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-658664