In this survey paper we discuss some tools and methods which are of use in quasiMonte Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis, Algebra and Number Theory, and Probability Theory. We do not provide a comprehensive survey of all tools, but focus on a few of them, including reproducing and covariance kernels, Littlewood-Paley theory, Riesz products, Mi...

Recently Knüsel (2008) proposed a new method of orthogonal rotation based on chi-square statistic, the Chisquaremax criterion. However, its performance has not yet been evaluated for the effect of outliers. Thus, we assessed the factorial model with Chisquaremax criterion for the effect of outliers using Monte Carlo simulation techniques in different scenarios. The efficiency of covariance matr...

We develop a new approach for pricing both continuous-time and discretetime American options which is based on the fact that any American option is equivalent to a European one with a consumption process involved. This approach admits the construction of an upper bound (a lower bound) on the true price using some lower bound (an upper bound) by Monte Carlo simulation. A number of effective esti...