Revisiting integral functionals of geometric Brownian motion

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 \(\mu\in\mathbb{R}\), \(\sigma > 0\), and \((W_s )_s>0\) is a standard Brownian motion. Specifically, we calculate the Laplace transform in \(t\) of the cumulative...

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Bibliographic Details
Published in:arXiv.org 2020-01
Main Authors: Boguslavskaya, Elena, Vostrikova, Lioudmila
Format: Article
Language:English
Subjects:
Brownian motion
Distribution functions
Economic models
Integrals
Laplace transforms
Probability density functions
Online Access:Get full text
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Summary: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 \(\mu\in\mathbb{R}\), \(\sigma > 0\), 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.
ISSN:2331-8422