Dimension-wise integration of high-dimensional functions with applications to finance

We present a new general class of methods for the computation of high-dimensional integrals. The quadrature schemes result by truncation and discretization of the anchored-ANOVA decomposition. They are designed to exploit low effective dimensions and include sparse grid methods as special case. To derive bounds for the resulting modelling and discretization errors, we introduce effective dimensions for the anchored-ANOVA decomposition. We show that the new methods can be applied in locally adaptive and dimension-adaptive ways and demonstrate their efficiency by numerical experiments with high-dimensional integrals from finance.