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.
Complete list of metadatas

Cited literature [27 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02461094
Contributor : Lioudmila Vostrikova <>
Submitted on : Thursday, January 30, 2020 - 2:25:40 PM
Last modification on : Saturday, February 1, 2020 - 1:48:37 AM

Files

Exp_func_revisiting_BV_final.p...
Files produced by the author(s)

Identifiers

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

Collections

Citation

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

Share

Metrics

Record views

12

Files downloads

14