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

Authors:
Giray Ökten;Bruno Tuffin;Vadim Burago
Affiliations:
Department of Mathematics, Florida State University, Tallahassee, FL;IRISA-INRIA, Rennes Cedex, France;Laboratory of Applied Mathematics, Pacific Fisheries Research Center (TINRO-Center), Vladivostok, Russia
Venue:
Journal of Complexity
Year:
2006

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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.