Exact simulation of the first-passage time of diffusions

2017/05/19 by Herrmann, Samuel, Zucca, Cristina · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1705.06881

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.

Cited by

• The hybrid exact scheme for the simulation of first-passage times of jump-diffusions with time-dependent thresholds
• First-passage time for PDifMPs: an Exact simulation approach for time-varying thresholds

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