Lattice Rules for Multiple Integration

Numerical methods for stochastic optimization often involve as basic steps the calculation of probabilities and of expected values in a multivariate setting. For this purpose, efficient routines for multidimensional numerical integration are needed. We discuss here a class of quasi-Monte Carlo methods which have been developed recently and which yield powerful tools for multiple integration. For a general background on quasi-Monte Carlo methods we refer to the survey articles of Niederreiter [12], [15] and to the forthcoming book [18].