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Exact simulation for multivariate Itô diffusions

Part of: Combinatorics, graph theory, probability theory, statistics Equilibrium statistical mechanics Functional-differential and differential-difference equations Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  03 December 2020

Jose Blanchet  and
Fan Zhang
Jose Blanchet*
Affiliation:
Stanford University
Fan Zhang*
Affiliation:
Stanford University
*
*Postal address: Huang Engineering Center, 475 Via Ortega, Stanford, CA 94305, United States.
*Postal address: Huang Engineering Center, 475 Via Ortega, Stanford, CA 94305, United States.
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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.

Keywords

Exact simulationstochastic differential equationBrownian motionMonte Carlo method

MSC classification

Primary: 34K50: Stochastic functional-differential equations 65C05: Monte Carlo methods 82B80: Numerical methods (Monte Carlo, series resummation, etc.)
Secondary: 97K60: Distributions and stochastic processes
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 4 , December 2020 , pp. 1003 - 1034
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Copyright
© Applied Probability Trust 2020

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