Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Hitting distributions of geometric Brownian motion

T. ByczkowskiM. Ryznar — 2006

Studia Mathematica

Let τ be the first hitting time of the point 1 by the geometric Brownian motion X(t) = x exp(B(t) - 2μt) with drift μ ≥ 0 starting from x > 1. Here B(t) is the Brownian motion starting from 0 with EB²(t) = 2t. We provide an integral formula for the density function of the stopped exponential functional A ( τ ) = 0 τ X ² ( t ) d t and determine its asymptotic behaviour at infinity. Although we basically rely on methods developed in [BGS], the present paper covers the case of arbitrary drifts μ ≥ 0 and provides a significant...

Page 1

Download Results (CSV)