Multilevel Monte Carlo by using the Halton sequence

Nagy Shady Ahmed (), El-Beltagy Mohamed A. () and Wafa Mohamed ()
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Nagy Shady Ahmed: Engineering Mathematics and Physics Department, Engineering Faculty, Cairo University, Giza12613, Egypt
El-Beltagy Mohamed A.: Engineering Mathematics and Physics Department, Engineering Faculty, Cairo University, Giza12613, Egypt
Wafa Mohamed: Engineering Mathematics and Physics Department, Engineering Faculty, Cairo University, Giza12613, Egypt

Monte Carlo Methods and Applications, 2020, vol. 26, issue 3, 193-203

Abstract: Monte Carlo (MC) simulation depends on pseudo-random numbers. The generation of these numbers is examined in connection with the Brownian motion. We present the low discrepancy sequence known as Halton sequence that generates different stochastic samples in an equally distributed form. This will increase the convergence and accuracy using the generated different samples in the Multilevel Monte Carlo method (MLMC). We compare algorithms by using a pseudo-random generator and a random generator depending on a Halton sequence. The computational cost for different stochastic differential equations increases in a standard MC technique. It will be highly reduced using a Halton sequence, especially in multiplicative stochastic differential equations.

Keywords: Stochastic differential equation; Monte Carlo techniques; low discrepancy sequences; multilevel Monte Carlo method (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/mcma-2020-2065

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