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The integral of geometric Brownian motion. (English) Zbl 0980.60103

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.

MSC:

60J65 Brownian motion
91B28 Finance etc. (MSC2000)
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