A new approach to unbiased estimation for SDE's

TL;DR

This paper presents a novel randomization method for creating unbiased estimators of SDE path functionals, achieving finite variance and square root convergence rate under certain conditions.

Contribution

Introduces a new unbiased estimation technique for SDE expectations using a randomization approach related to multi-level Monte Carlo.

Findings

Achieves finite variance unbiased estimators.

Provides square root convergence rate under specific strong error conditions.

Applicable to path functionals with strong error order > 1/2.

Abstract

In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to multi-level Monte Carlo and provides a simple mechanism for constructing a finite variance unbiased estimator with "square root convergence rate" whenever one has available a scheme that produces strong error of order greater than 1/2 for the path functional under consideration.