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

  • Book
  • © 2011

Overview

Authors:
  1. Markus Holtz

    1. , Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Markus Holtz
    Pages 1-9

  3. Dimension-wise Decompositions

    • Markus Holtz
    Pages 11-27

  4. Dimension-wise Quadrature

    • Markus Holtz
    Pages 29-50

  5. Sparse Grid Quadrature

    • Markus Holtz
    Pages 51-76

  6. Dimension Reduction and Smoothing

    • Markus Holtz
    Pages 77-100

  7. Validation and Applications

    • Markus Holtz
    Pages 101-151

  8. Summary and Conclusions

    • Markus Holtz
    Pages 153-156

  9. Back Matter

    Pages 157-189
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Keywords

About this book

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.

Authors and Affiliations

  • , Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Markus Holtz

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

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