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On the quantiles of the Brownian motion and their hitting times

Dassios, Angelos (2005) On the quantiles of the Brownian motion and their hitting times. Bernoulli, 11 (1). pp. 29-36. ISSN 1350-7265

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Abstract

The distribution of the Æ-quantile of a Brownian motion on an interval [0, t] has been obtained motivated by a problem in financial mathematics. In this paper we generalize these results by calculating an explicit expression for the joint density of the Æ-quantile of a standard Brownian motion, its first and last hitting times and the value of the process at time t. Our results can easily be generalized to a Brownian motion with drift. It is shown that the first and last hitting times follow a transformed arcsine law.

Item Type: Article
Official URL: http://projecteuclid.org/DPubS?service=UI&version=...
Additional Information: © 2007 Bernoulli Society for Mathematical Statistics and Probability
Library of Congress subject classification: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Sets: Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 06 Nov 2007
URL: http://eprints.lse.ac.uk/2845/

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