Exact simulation of the first-passage time of diffusions
Abstract
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For efficiency reasons, it is particularly challenging to simulate directly this hitting time by avoiding to construct the whole paths. In the Brownian case, the distribution of the first-passage time is explicitly known and can be easily used for simulation purposes. The authors introduce a new rejection sampling algorithm which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes. The efficiency of the method, which is essentially based on Girsanov's transformation , is described through theoretical results and numerical examples.
Keywords
Cite
@article{arxiv.1705.06881,
title = {Exact simulation of the first-passage time of diffusions},
author = {Samuel Herrmann and Cristina Zucca},
journal= {arXiv preprint arXiv:1705.06881},
year = {2017}
}