Multilevel path simulation for weak approximation schemes

Denis Belomestny and 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 L\'evy driven stochastic differential equations, and show that, given a weak convergence of order $\alpha\geq 1/2,$ 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.

Date: 2014-06, Revised 2014-10
New Economics Papers: this item is included in nep-cmp
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1406.2581

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