Revisiting integral functionals of geometric Brownian motion

01/31/2020

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by   Elena Boguslavskaya, et al.

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In this paper we revisit the integral functional of geometric Brownian motion I_t= ∫_0^t e^-(μ s +σ W_s)ds, where μ∈R, σ > 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.