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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis


CiteScore 2018: 0.66

SCImago Journal Rank (SJR) 2018: 0.319
Source Normalized Impact per Paper (SNIP) 2018: 0.720

Mathematical Citation Quotient (MCQ) 2017: 0.25

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1569-3961
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Volume 16, Issue 2

Issues

The Multilevel Monte Carlo method used on a Lévy driven SDE

Henning Marxen
  • Department of Mathematics, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany. E-mail:
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Published Online: 2010-07-12 | DOI: https://doi.org/10.1515/mcma.2010.007

Abstract

In this paper the Multilevel Monte Carlo method introduced by Giles [Operations Research 56: 607–617, 2008] is refined by the extended complexity theorem and applied to Lévy process driven SDEs. The restricted approximate Euler scheme is used to simulate the SDEs. Recent results about the convergence by Fournier [ArXiv e-prints: 2009] and by Jacod, Kurtz, Máléard and Protter [Annales de l'Institut Henri Poincare (B) Probability and Statistics 41: 523–558, 2005] are used. The theoretical results are illustrated by numerical simulations.

Keywords.: Lévy processes; stochastic differential equations; Monte Carlo; Multilevel Monte Carlo; complexity theorem; Euler scheme; Blumenthal–Getoor index

About the article

Received: 2009-12-11

Revised: 2010-05-18

Published Online: 2010-07-12

Published in Print: 2010-07-01


Citation Information: Monte Carlo Methods and Applications, Volume 16, Issue 2, Pages 167–190, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma.2010.007.

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