On the quantiles of Brownian motion and their hitting times

Angelos Dassios

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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.

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Bernoulli, Volume 11, Number 1 (2005), 29-36.

First available in Project Euclid: 7 March 2005

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arcsine law hitting times quantiles of Brownian motion


Dassios, Angelos. On the quantiles of Brownian motion and their hitting times. Bernoulli 11 (2005), no. 1, 29--36. doi:10.3150/bj/1110228240.

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