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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2019077
Keywords: Exit time, Brownian motion, diffusion processes, Girsanov’s transformation, rejection sampling, exact simulation, randomized algorithm, conditioned Brownian motion
@article{M2AN_2020__54_3_811_0,
author = {Herrmann, Samuel and Zucca, Cristina},
title = {Exact simulation of first exit times for one-dimensional diffusion processes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {811--844},
year = {2020},
publisher = {EDP Sciences},
volume = {54},
number = {3},
doi = {10.1051/m2an/2019077},
mrnumber = {4080787},
zbl = {07197800},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2019077/}
}
TY - JOUR AU - Herrmann, Samuel AU - Zucca, Cristina TI - Exact simulation of first exit times for one-dimensional diffusion processes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 811 EP - 844 VL - 54 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2019077/ DO - 10.1051/m2an/2019077 LA - en ID - M2AN_2020__54_3_811_0 ER -
%0 Journal Article %A Herrmann, Samuel %A Zucca, Cristina %T Exact simulation of first exit times for one-dimensional diffusion processes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 811-844 %V 54 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2019077/ %R 10.1051/m2an/2019077 %G en %F M2AN_2020__54_3_811_0
Herrmann, Samuel; Zucca, Cristina. Exact simulation of first exit times for one-dimensional diffusion processes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 3, pp. 811-844. doi: 10.1051/m2an/2019077
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