| Issue |
ESAIM: M2AN
Volume 54, Number 3, May-June 2020
|
|
|---|---|---|
| Page(s) | 811 - 844 | |
| DOI | https://doi.org/10.1051/m2an/2019077 | |
| Published online | 01 April 2020 | |
Exact simulation of first exit times for one-dimensional diffusion processes
1
Institut de Mathématiques de Bourgogne – UMR 5584, CNRS, Université de Bourgogne Franche-Comté, F-21000 Dijon, France
2
Department of Mathematics “G. Peano”, University of Torino, Via Carlo Alberto 10, 10123 Turin, Italy
* Corresponding author: samuel.herrmann@u-bourgogne.fr
Received:
9
May
2019
Accepted:
24
October
2019
The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability… The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study are the Girsanov transformation, the convergent series method for the simulation of random variables and the classical rejection sampling. The efficiency of the method is described through theoretical results and numerical examples.
Mathematics Subject Classification: 65C05 / 65N75 / 60G40
Key words: Exit time / Brownian motion / diffusion processes / Girsanov’s transformation / rejection sampling / exact simulation / randomized algorithm / conditioned Brownian motion
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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