- Volume 11, Number 1 (2005), 29-36.
On the quantiles of Brownian motion and their hitting times
The distribution of the α-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 α-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.
Bernoulli, Volume 11, Number 1 (2005), 29-36.
First available in Project Euclid: 7 March 2005
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Dassios, Angelos. On the quantiles of Brownian motion and their hitting times. Bernoulli 11 (2005), no. 1, 29--36. doi:10.3150/bj/1110228240. https://projecteuclid.org/euclid.bj/1110228240