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arXiv · 2001.11861

Revisiting integral functionals of geometric Brownian motion

Elena Boguslavskaya·Lioudmila Vostrikova
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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 $\mu\in\mathbb{R}$, $\sigma > 0$, 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.

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Elena Boguslavskaya, Lioudmila Vostrikova. 2020-01-31. Revisiting integral functionals of geometric Brownian motion. https://arxiv.org/abs/2001.11861

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