Advances in Decision Sciences

Advances in Decision Sciences / 1999 / Article

Open Access

Volume 3 |Article ID 693018 | https://doi.org/10.1155/S1173912699000036

Andreas Pechtl, "Distributions of occupation times of Brownian motion with drift", Advances in Decision Sciences, vol. 3, Article ID 693018, 22 pages, 1999. https://doi.org/10.1155/S1173912699000036

Distributions of occupation times of Brownian motion with drift

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.

Copyright © 1999 Hindawi Publishing Corporation. 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.


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