Bernoulli

On the quantiles of Brownian motion and their hitting times

Angelos Dassios

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 7 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1110228240

Digital Object Identifier
doi:10.3150/bj/1110228240

Mathematical Reviews number (MathSciNet)
MR2121453

Zentralblatt MATH identifier
1062.60079

Keywords
arcsine law hitting times quantiles of Brownian motion

Citation

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


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