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Exact Sampling for Multivariate Diffusions

Presented by: 
Jose Blanchet Columbia University, Stanford University
Friday 7th July 2017 - 11:00 to 11:45
INI Seminar Room 1
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 transformation, called Lamperti transformation, can be applied in general only in one dimension. So, completely different ideas are required for 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 one hand, and multilevel Monte Carlo on the other. (Joint work with Fan Zhang.)
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons