Variance reduction for discretised diffusions via regression

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 (${\epsilon }^{-3}$ in the case of a first order scheme and ${\epsilon }^{-2.5}$ in the case of a second order scheme) can be reduced down to ${\epsilon }^{-2+\delta }$ for any $\delta \in [0,0.25)$ with $\epsilon$ being the precision to be achieved. These theoretical results are illustrated by several numerical examples.

References in corpus (2)

• An operator approach for Markov chain weak approximations with an application to infinite activity Lévy driven SDEs
• A Discrete-Time Clark-Ocone Formula and its Application to an Error Analysis

Cited by in corpus (5)

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• Neural variance reduction for stochastic differential equations
• Regression-based variance reduction approach for strong approximation schemes
• Stratified regression-based variance reduction approach for weak approximation schemes
• Truncated control variates for weak approximation schemes