On the quantiles of Brownian motion and their hitting times
Dassios, Angelos
Bernoulli, Tome 11 (2005) no. 1, p. 29-36 / Harvested from Project Euclid
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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.
Publié le : 2005-01-14
Classification:  arcsine law,  hitting times,  quantiles of Brownian motion 
@article{1110228240,
     author = {Dassios, Angelos},
     title = {On the quantiles of Brownian motion and their hitting times},
     journal = {Bernoulli},
     volume = {11},
     number = {1},
     year = {2005},
     pages = { 29-36},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1110228240}
}

Dassios, Angelos. On the quantiles of Brownian motion and their hitting times. Bernoulli, Tome 11 (2005) no. 1, pp.  29-36. http://gdmltest.u-ga.fr/item/1110228240/