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

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Springer Science & Business Media, Oct 22, 2010 - Mathematics - 192 pages
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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.
 

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Contents

1 Introduction
1
2 Dimensionwise Decompositions
10
3 Dimensionwise Quadrature
29
4 Sparse Grid Quadrature
51
5 Dimension Reduction and Smoothing
77
6 Validation and Applications
101
7 Summary and Conclusions
152
A Discrepancy and Tractability
157
Index
179
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About the author (2010)

• 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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