Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance

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.

About the author

• 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

Summary

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.

Product details

• Authors: Markus Holtz
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 16.11.2012
• EAN: 9783642265631
• ISBN: 978-3-642-26563-1
• No. of pages: 192
• Dimensions: 155 mm x 11 mm x 235 mm
• Weight: 312 g
• Illustrations: VIII, 192 p. 32 illus.
• Series: Lecture Notes in Computational Science and Engineering; Lecture Notes in Computational Science and Engineering
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; C, Angewandte Mathematik, Mathematics and Statistics, Finance & accounting, Computational Mathematics and Numerical Analysis, Computer mathematics, Economics, Mathematical, Quantitative Finance, Mathematics in Business, Economics and Finance