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A central limit theorem and improved error bounds for a hybrid-Monte Carlo sequence with applications in computational finance

Giray Ökten 1 Bruno Tuffin 2 Vadim Burago 3
2 ARMOR - Architectures and network models
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes, Ecole Nationale Supérieure des Télécommunications de Bretagne
Abstract : In problems of moderate dimensions, the quasi-Monte Carlo method usually provides better estimates than the Monte Carlo method. However, as the dimension of the problem increases, the advantages of the quasi-Monte Carlo method diminish quickly. A remedy for this problem is to use hybrid sequences; sequences that combine pseudorandom and low-discrepancy vectors. In this paper we discuss a particular hybrid sequence called the mixed sequence. We will provide improved discrepancy bounds for this sequence and prove a central limit theorem for the corresponding estimator. We will also provide numerical results that compare the mixed sequence with the Monte Carlo and randomized quasi-Monte Carlo methods.
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https://hal.inria.fr/inria-00070407
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 8:24:03 PM
Last modification on : Thursday, February 11, 2021 - 2:48:03 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:08:29 PM

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  • HAL Id : inria-00070407, version 1

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Giray Ökten, Bruno Tuffin, Vadim Burago. A central limit theorem and improved error bounds for a hybrid-Monte Carlo sequence with applications in computational finance. [Research Report] RR-5600, INRIA. 2005, pp.28. ⟨inria-00070407⟩

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