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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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hal-02461094 , version 1 (30-01-2020)

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Elena Boguslavskaya, Lioudmila Vostrikova. Revisiting integral functionals of geometric Brownian motion. 2020. ⟨hal-02461094⟩
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