Lemaire, Vincent; Pagès, Gilles Multilevel Richardson-Romberg extrapolation. (English) Zbl 1383.65003 Bernoulli 23, No. 4A, 2643-2692 (2017). The paper proposes to improve the standard multilevel Monte Carlo (MLMC) paradigm by combining the MLMC estimator and the multistep Richardson-Romberg extrapolation with a general parametrized framework to formalize the optimization of a biased Monte Carlo simulation based on the \(L^{2}\)-error minimization. As examples of applications, a weak expansion of the error at any order is established for the time discretization of stochastic processes and the nested Monte Carlo method. Some numerical experimental results are presented. Reviewer: Hang Lau (Montréal) Cited in 1 ReviewCited in 21 Documents MSC: 65C05 Monte Carlo methods 60-08 Computational methods for problems pertaining to probability theory 91G60 Numerical methods (including Monte Carlo methods) Keywords:Euler scheme; multilevel Monte Carlo estimator; multistep; nested Monte Carlo method; option pricing; Richardson-Romberg extrapolation; numerical experimental results PDFBibTeX XMLCite \textit{V. Lemaire} and \textit{G. Pagès}, Bernoulli 23, No. 4A, 2643--2692 (2017; Zbl 1383.65003) Full Text: DOI arXiv Euclid