Distributions of occupation times of Brownian motion with drift

Andreas Pechtl

25 citations0/0 files storedJournal of Applied Mathematics and Decision Sciences

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

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.

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2007Brownian Motion and Stochastic Calculus 1981Martingales and stochastic integrals in the theory of continuous trading 1989Brownian Motion and Stochastic Calculus.1989Security Markets: Stochastic Models.1988Security Markets: Stochastic Models 1995The Distribution of the Quantile of a Brownian Motion with Drift and the Pricing of Related Path-Dependent Options 1995Some Formulae for a New Type of Path-Dependent Option 1990Security Markets, Stochastic Models.

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