Unbiased Monte Carlo estimate of stochastic differential equations expectations

TL;DR

This paper introduces a Monte Carlo method for unbiased estimation of expectations of solutions to stochastic differential equations, extending previous techniques to multidimensional cases and incorporating variance reduction via interacting particle systems.

Contribution

It presents a novel unbiased Monte Carlo approach for multidimensional SDE expectations and develops a variance reduction technique using interacting particle systems.

Findings

Unbiased Monte Carlo estimator for multidimensional SDEs.

Effective variance reduction through interacting particle systems.

Extension of previous methods to more general SDEs.

Abstract

We develop a pure Monte Carlo method to compute $E(g(X_T))$ where $g$ is a bounded and Lipschitz function and $X_t$ an Ito process. This approach extends a previously proposed method to the general multidimensional case with a SDE with varying coefficients. A variance reduction method relying on interacting particle systems is also developped.