Journal of Applied Mathematics and Decision Sciences
Volume 3 (1999), Issue 1, Pages 41-62

Distributions of occupation times of Brownian motion with drift

Andreas Pechtl

Center of Asset Pricing and Financial Products Development, Deutsche Genossenschaftsbank Frankfurt am Main, Am Platz der Republik, Frankfurt am Main D–60325, Germany

Copyright © 1999 Andreas Pechtl. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this paper is to present a survey of recent developments concerning the distributions of occupation times of Brownian motion and their applications in mathematical finance. The main result is a closed form version for Akahori's generalized arc-sine law which can be exploited for pricing some innovative types of options in the Black & Scholes model. Moreover a straightforward proof for Dassios' representation of the α -quantile of Brownian motion with drift shall be provided.