Regression-based variance reduction approach for strong approximation schemes

Abstract

In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the terminal functionals. In this way the complexity order of the standard Monte Carlo algorithm (${\epsilon }^{-3}$) can be reduced down to ${\epsilon }^{-2}\sqrt{\left|\log (\epsilon )\right|}$ in case of the Euler scheme with $\epsilon$ being the precision to be achieved. These theoretical results are illustrated by several numerical examples.

arXiv admin note: text overlap with arXiv:1510.03141