Journal of Applied Mathematics and Decision Sciences
Volume 3 (1999), Issue 1, Pages 41-62
doi:10.1155/S1173912699000036
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.