Multilevel Monte Carlo EM scheme for MV-SDEs with small noise

TL;DR

This paper develops a multilevel Monte Carlo Euler scheme to efficiently estimate the variance of coupled paths in McKean-Vlasov SDEs with small noise, improving over standard methods.

Contribution

It introduces a novel multilevel Monte Carlo approach combined with Euler discretization for small noise McKean-Vlasov SDEs, enhancing computational efficiency.

Findings

More accurate variance estimation for small noise SDEs

Reduced computational cost compared to standard Monte Carlo

Demonstrated efficiency through numerical experiments

Abstract

In this paper, we estimate the variance of two coupled paths derived with the Multilevel Monte Carlo method combined with the Euler Maruyama discretization scheme for the simulation of McKean-Vlasov stochastic differential equations with small noise. The result often translates into a more efficient method than the standard Monte Carlo method combined with algorithms tailored to the small noise setting.