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On the quantiles of the Brownian motion and their hitting times

By Angelos Dassios


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

Topics: QA Mathematics, HA Statistics
Publisher: Bernoulli Society for Mathematical Statistics and Probability
Year: 2005
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Provided by: LSE Research Online
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