This book deals with the numerical analysis and efficient numerical treatment of high-dimensional integrals using sparse grids and other dimension-wise integration techniques with applications to finance and insurance. The book focuses on providing insights into the interplay between coordinate transformations, effective dimensions and the convergence behaviour of sparse grid methods. The techniques, derivations and algorithms are illustrated by many examples, figures and code segments. Numerical experiments with applications from finance and insurance show that the approaches presented in this book can be faster and more accurate than (quasi-) Monte Carlo methods, even for integrands with hundreds of dimensions.

Includes supplementary material: sn.pub/extras

Autorentext

Scientific employee at the Institute for Numerical Simulation at the University of Bonn (July 2004 - January 2009) Involved in several teaching activities and research projects in the area of computational finance partly in close cooperation with financial institutions Since January 2009 at head office of Baloise Group working on the introduction of stochastic models for life insurance portfolios