Variance reduced multilevel path simulation: going beyond the complexity $\varepsilon^{-2}$

Denis Belomestny and Tigran Nagapetyan

Papers from arXiv.org

Abstract: In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level zero. We show that, under a proper choice of control variates, one can reduce the complexity order of the modified MLMC algorithm down to $\varepsilon^{-2+\delta}$ for any $\delta\in [0,1)$ with $\varepsilon$ being the precision to be achieved. These theoretical results are illustrated by several numerical examples.

Date: 2014-12, Revised 2017-03
New Economics Papers: this item is included in nep-cmp and nep-rmg
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