Advances in Decision Sciences
Volume 3 (1999), Issue 1, Pages 41-62
doi:10.1155/S1173912699000036
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
Abstract
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.