AN INTRODUCTION TO MULTILEVEL MONTE CARLO METHODS

Abstract

In recent years there has been very substantial growth in stochastic modelling in many application areas, and this has led to much greater use of Monte Carlo methods to estimate expected values of output quantities from stochastic simulation. However, such calculations can be expensive when the cost of individual stochastic simulations is very high. Multilevel Monte Carlo greatly reduces the computational cost by performing most simulations with low accuracy at a correspondingly low cost, with relatively few being performed at high accuracy and a high cost. This article reviews the key ideas behind the multilevel Monte Carlo method. Some applications are discussed to illustrate the flexibility and generality of the approach, and the challenges in its numerical analysis.