Revisiting integral functionals of geometric Brownian motion

Elena Boguslavskaya and Lioudmila Vostrikova ()
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Lioudmila Vostrikova: LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: exponential integral functional; Laplace transform; Geometric Brownian motion (search for similar items in EconPapers)
Date: 2020-01-30
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