Blanchet J, Zhang F. Exact simulation for multivariate Itô diffusions. Advances in Applied Probability. 2020;52(4):1003-1034. doi:10.1017/apr.2020.39
Abstract
We provide the first generic exact simulation algorithm for multivariate diffusions. Current exact sampling algorithms for diffusions require the existence of a transformation which can be used to reduce the sampling problem to the case of a constant diffusion matrix and a drift which is the gradient of some function. Such a transformation, called the Lamperti transformation, can be applied in general only in one dimension. So, completely different ideas are required for the exact sampling of generic multivariate diffusions. The development of these ideas is the main contribution of this paper. Our strategy combines techniques borrowed from the theory of rough paths, on the one hand, and multilevel Monte Carlo on the other.
Authors
Jose Blanchet, Fan Zhang
Publication date
2020/12
Journal
Advances in Applied Probability
Volume
52
Issue
4
Pages
1003-1034
Publisher
Cambridge University Press
