Dassios, Angelos (2005) On the quantiles of the Brownian motion and their hitting times. Bernoulli, 11 (1). pp. 29-36. ISSN 1350-7265
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 |
| Uncontrolled Keywords: | arcsine law, hitting times, quantiles of Brownian motion |
| Library of Congress subject classification: | Q Science > QA Mathematics H Social Sciences > HA Statistics |
| Sets: | Departments > Statistics |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/2845/ |
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