In this paper we revisit the integral functional of geometric Brownian motion $I_t= int_0^t e^{-(mu s +sigma W_s)}ds$, where $muinmathbb{R}$, $sigma > 0$, and $(W_s )_s>0$ is a standard Brownian motion. Specifically, we calculate the Laplace transform in $t$ of the cumulative distribution function and of the probability density function of this functional.
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