The Multilevel Monte Carlo method used on a Lévy driven SDE

Marxen Henning
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Marxen Henning: Department of Mathematics, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany. E-mail: marxen@mathematik.uni-kl.de

Monte Carlo Methods and Applications, 2010, vol. 16, issue 2, 167-190

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 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1515/mcma.2010.007

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