# 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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Cited literature [27 references]

https://hal.archives-ouvertes.fr/hal-02461094
Contributor : Lioudmila Vostrikova <>
Submitted on : Thursday, January 30, 2020 - 2:25:40 PM
Last modification on : Wednesday, September 2, 2020 - 4:40:48 PM

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Exp_func_revisiting_BV_final.p...
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### Identifiers

• HAL Id : hal-02461094, version 1
• ARXIV : 2001.11861

### Citation

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

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