Ebook: 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.

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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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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.
Content:
Front Matter....Pages i-viii
Introduction....Pages 1-9
Dimension-wise Decompositions....Pages 11-27
Dimension-wise Quadrature....Pages 29-50
Sparse Grid Quadrature....Pages 51-76
Dimension Reduction and Smoothing....Pages 77-100
Validation and Applications....Pages 101-151
Summary and Conclusions....Pages 153-156
Back Matter....Pages 157-189

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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.
Content:
Front Matter....Pages i-viii
Introduction....Pages 1-9
Dimension-wise Decompositions....Pages 11-27
Dimension-wise Quadrature....Pages 29-50
Sparse Grid Quadrature....Pages 51-76
Dimension Reduction and Smoothing....Pages 77-100
Validation and Applications....Pages 101-151
Summary and Conclusions....Pages 153-156
Back Matter....Pages 157-189
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