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
VIRTA submission year: 2019
JUFO rating: 1