Low-Discrepancy Simulation

Summary. This article presents a survey of low-discrepancy sequences and their applications to quasi-Monte Carlo methods for multidimensional numerical integra-tion. Quasi-Monte Carlo methods are deterministic versions of Monte Carlo methods which outperform Monte Carlo methods for many types of integrals and have thus been found enormously useful in computational finance. First a general background on quasi-Monte Carlo methods is given. Then we describe principles for the con-struction of low-discrepancy sequences, with a special emphasis on the currently most powerful constructions based on the digital method and the theory of (T, s)-sequences. Next, the important concepts of effective dimension and tractability are discussed. A synopsis of randomized quasi-Monte Carlo methods and their applica-tions to computational finance concludes the article.