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Multilevel path simulation for weak approximation schemes

: Belomestny, D.; Nagapetyan, T; Shiryaev, V.

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Online im WWW, 2014, arXiv:1406.2581, 24 pp.
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Fraunhofer ITWM ()

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 α≥1/2, the complexity of the corresponding "weak" MLMC estimate is of order ε−2log2(ε). The numerical performance of the new "weak" MLMC method is illustrated by several numerical examples.