Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

Peter Kloeden (), Andreas Neuenkirch () and Raffaella Pavani ()

Annals of Operations Research, 2011, vol. 189, issue 1, 255-276

Abstract: We adopt the multilevel Monte Carlo method introduced by M. Giles (Multilevel Monte Carlo path simulation, Oper. Res. 56(3):607–617, 2008 ) to SDEs with additive fractional noise of Hurst parameter H>1/2. For the approximation of a Lipschitz functional of the terminal state of the SDE we construct a multilevel estimator based on the Euler scheme. This estimator achieves a prescribed root mean square error of order ε with a computational effort of order ε −2 . Copyright Springer Science+Business Media, LLC 2011

Keywords: SDEs with additive noise; Fractional Brownian motion; Multilevel Monte Carlo; Euler scheme; Malliavin calculus (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10479-009-0663-8

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