A1 Journal article (refereed)
On first exit times and their means for Brownian bridges (2019)

Geiss, C., Luoto, A., & Salminen, P. (2019). On first exit times and their means for Brownian bridges. Journal of Applied Probability, 56(3), 701-722. https://doi.org/10.1017/jpr.2019.42

JYU authors or editors

Publication details

All authors or editors: Geiss, Christel; Luoto, Antti; Salminen, Paavo

Journal or series: Journal of Applied Probability

ISSN: 0021-9002

eISSN: 1475-6072

Publication year: 2019

Volume: 56

Issue number: 3

Pages range: 701-722

Publisher: Cambridge University Press; Applied Probability Trust

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1017/jpr.2019.42

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1711.06107

Abstract

For a Brownian bridge from 0 to y, we prove that the mean of the first exit time from the interval (−h, h), h > 0, behaves as O(h2) when h ↓ 0. Similar behaviour is also seen to hold for the three-dimensional Bessel bridge. For the Brownian bridge and threedimensional 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 provide a detailed proof of an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.

Keywords: mathematics; stochastic processes; Markov chains

Free keywords: Bessel process; Black-Scholes model; Brownian motion; diffusion process; h-transform; last exit time; Poisson summation formula

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2019

JUFO rating: 1