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

  • Markus Holtz
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 77)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Markus Holtz
    Pages 1-9
  3. Markus Holtz
    Pages 11-27
  4. Markus Holtz
    Pages 29-50
  5. Markus Holtz
    Pages 51-76
  6. Markus Holtz
    Pages 77-100
  7. Markus Holtz
    Pages 101-151
  8. Markus Holtz
    Pages 153-156
  9. Back Matter
    Pages 157-189

About this book

Introduction

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.

Keywords

ANOVA decomposition computational finance effective dimension numerical integration sparse grids

Authors and affiliations

  • Markus Holtz
    • 1
  1. 1., Institut für Numerische SimulationUniversität BonnBonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-16004-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-16003-5
  • Online ISBN 978-3-642-16004-2
  • Series Print ISSN 1439-7358
  • About this book