2014/12/12 by Denis Belomestny, Belomestny, Denis, Tigran Nagapetyan +1
Engineering · Mathematics · Physics and Astronomy · #65C05 #65C30 #Advanced Numerical Methods in Computational Mathematics #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Model Reduction and Neural Networks #Numerical methods for differential equations #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1412.4045
openalex publication_date 2014/12/12 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
In this paper a novel modification of the multilevel Monte Carlo approach,\nallowing for further significant complexity reduction, is proposed. The idea of\nthe modification is to use the method of control variates to reduce variance at\nlevel zero. We show that, under a proper choice of control variates, one can\nreduce the complexity order of the modified MLMC algorithm down to\n\ε-2+\δ for any \δ\∈ [0,1) with \ε being\nthe precision to be achieved. These theoretical results are illustrated by\nseveral numerical examples.\n