Revisiting integral functionals of geometric Brownian motion

2020/01/31 by Elena Boguslavskaya, Boguslavskaya, Elena, Vostrikova, Lioudmila
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #General Finance (q-fin.GN) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2001.11861

openalex publication_date 2020/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we revisit the integral functional of geometric Brownian motion I_t= ∫₀^t e^{-(μs +σW_s)}ds, where μ∈ℝ, σ> 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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