On the quantiles of the Brownian motion and their hitting times

Dassios, Angelos ORCID: 0000-0002-3968-2366 (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
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics H Social Sciences > HA Statistics
Date Deposited:	06 Nov 2007
Last Modified:	13 Sep 2024 21:58
URI:	http://eprints.lse.ac.uk/id/eprint/2845

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