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arXiv · 1406.2581

Multilevel path simulation for weak approximation schemes

Denis Belomestny·Tigran Nagapetyan
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Abstract

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify this general idea in the case of weak Euler scheme for Lévy driven stochastic differential equations, and show that, given a weak convergence of order $α\geq 1/2,$ the complexity of the corresponding "weak" MLMC estimate is of order $\varepsilon^{-2}\log ^{2}(\varepsilon).$ The numerical performance of the new "weak" MLMC method is illustrated by several numerical examples.

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Denis Belomestny, Tigran Nagapetyan. 2014-10-05. Multilevel path simulation for weak approximation schemes. https://arxiv.org/abs/1406.2581

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