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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
Received: 2009-12-11
Revised: 2010-05-18
Published Online: 2010-07-12
Published in Print: 2010-July
© de Gruyter 2010