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Pré-Publication, Document De Travail Année : 2017

Exact simulation of the first-passage time of diffusions

Cristina Zucca
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Résumé

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.
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Dates et versions

hal-01524814 , version 1 (18-05-2017)

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Samuel Herrmann, Cristina Zucca. Exact simulation of the first-passage time of diffusions. 2017. ⟨hal-01524814⟩
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