On the Acceleration of the Multi-Level Monte Carlo Method

Abstract

The multi-level Monte Carlo method proposed by M. Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper, a modified multi-level Monte Carlo estimator is proposed with significantly reduced computational costs. As the main result, it is proved that the modified estimator reduces the computational costs asymptotically by a factor $(p/\alpha {)}^2$ if weak approximation methods of orders $\alpha$ and $p$ are applied in case of computational costs growing with same order as variances decay.

References in corpus (3)

• Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correction
• Statistical Romberg extrapolation: A new variance reduction method and applications to option pricing
• Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise

Cited by in corpus (2)

• Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function
• Central Limit Theorem for the $\sigma$-antithetic multilevel Monte Carlo method