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2012•Journal of Mathematics and Computer ScienceOpen access

Monte Carlo Simulation For Numerical Integration Based On Antithetic Variance Reduction And Haltons Sequences

Farshid Mehrdoust

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Abstract

Many applications, for instance in finance and in physics, require the calculation of high dimensional integrals. The Monte Carlo and quasi Monte Carlo methods are frequently used to approximate them. In this paper, we propose a new quasi Monte Carlo algorithm based on antithetic variance reduction and Halton's sequences for numerical integration. Efficiency of the new algorithm compared to the standard Monte Carlo algorithm is shown using example.

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Many applications, for instance in finance and in physics, require the calculation of high dimensional integrals. The Monte Carlo and quasi Monte Carlo methods are frequently used to approximate them. In this paper, we propose a new quasi Monte Carlo algorithm based on antithetic variance reduction and Halton's sequences for numerical integration. Efficiency of the new algorithm compared to the standard Monte Carlo algorithm is shown using example.

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Available abstract

Many applications, for instance in finance and in physics, require the calculation of high dimensional integrals. The Monte Carlo and quasi Monte Carlo methods are frequently used to approximate them. In this paper, we propose a new quasi Monte Carlo algorithm based on antithetic variance reduction and Halton's sequences for numerical integration. Efficiency of the new algorithm compared to the standard Monte Carlo algorithm is shown using example.

Key concepts: Variance reduction, Monte Carlo method, Reduction (mathematics), Control variates, Variance (accounting), Monte Carlo integration, Quasi-Monte Carlo method, Statistics

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