Monte Carlo simulation for numerical integration based on antithetic variance reduction and Halton's sequences

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.