Dufresne, Daniel The integral of geometric Brownian motion. (English) Zbl 0980.60103 Adv. Appl. Probab. 33, No. 1, 223-241 (2001). Let \(B\) be a one-dimensional standard Brownian motion starting from the origin. The purpose of this paper is to find a new formula for the density function of \(A^{(\mu)}_t=\int^t_0e^{2\mu\tau+2B_{\tau}} d\tau\), where \(t>0\) and \(\mu\in R\). Several people have already derived different formulae for the density of \(A^{(\mu)}_t\). The new formula for the density derived in this paper is simpler than other formulae in the case when \(\mu\) is a nonnegative integer. Reviewer: Renming Song (Urbana) Cited in 4 ReviewsCited in 57 Documents MSC: 60J65 Brownian motion 91B28 Finance etc. (MSC2000) Keywords:Brownian motion; Bougerol’s identity; Asian options PDFBibTeX XMLCite \textit{D. Dufresne}, Adv. Appl. Probab. 33, No. 1, 223--241 (2001; Zbl 0980.60103) Full Text: DOI