Revisiting integral functionals of geometric Brownian motion
Abstract
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 µ ∈ R, σ > 0, and
$(W_s )_s>0 $i s 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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