On first exit times and their means for Brownian bridges.

A1 Journal article (refereed)


Internal Authors/Editors


Publication Details

List of Authors: Christel Geiss, Antti Luoto, Paavo Salminen
Publication year: 2019
Journal: Journal of Applied Probability
Volume number: 56
Issue number: 3
Start page: 701
End page: 722


Abstract

For a Brownian bridge from $0$ to $y$ we prove that the mean of the first exit time from interval $(-h,h), ,, h>0,$ behaves as $O(h^2)$ when $h downarrow 0.$ Similar behavior is seen to hold also for the 3-dimensional Bessel bridge. For Brownian bridge and 3-dimensional Bessel bridge this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to prove in detail an estimateneeded by Walsh to determine the convergence of the binomial tree scheme for European options.


Last updated on 2020-02-04 at 09:04