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
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 -quantile of Brownian motion with drift shall be provided.
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