Quasi Monte Carlo methods in numerical analysis and insurance

For high-dimensional numerical integration Quasi Monte Carlo methods are an appropriate tool. The approximation error can be estimated by the Koksma-Hlawka inequality which involves a certain concept of total variation of the integrand and the so-called discrepancy, measuring the distribution of the used point set in the unit cube.  We discuss various useful concepts of variation and of discrepancy as well as applications to integral equations of the Fredholm type. Furthermore, we consider applications for an insurance surplus process of the Sparre-Andersen type with surplus-dependent premiums. Analytical properties are studied and QMC methods are applied for obtaining solutions to relevant quantities. Numerical examples show that the speed of convergence is satisfactory. This is joint work M. Preischl and S. Thonhauser.