Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance [electronic resource] /
Holtz, Markus.author.
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.
Description based upon print version of record.
Preface; Contents; 1 Introduction; 2 Dimension-wise Decompositions; 2.1 Classical ANOVA Decomposition; 2.2 Anchored-ANOVA Decomposition; 3 Dimension-wise Quadrature; 3.1 Classical Multivariate Quadrature Methods; 3.2 Dimension-wise Quadrature Methods; 4 Sparse Grid Quadrature; 4.1 Sparse Grid Methods; 4.2 Optimal Sparse Grids in Weighted Spaces; 4.3 Relation to Dimension-wise Quadrature; 5 Dimension Reduction and Smoothing; 5.1 Dimension Reduction; 5.2 Domain Decomposition; 6 Validation and Applications; 6.1 Interest Rates Derivatives; 6.2 Path-dependent Options
6.3 Performance-dependent Options6.4 Asset-Liability Management in Life Insurance; 6.5 Summary and Discussion; 7 Summary and Conclusions; A Discrepancy and Tractability; A.1 Reproducing Kernel Hilbert Spaces; A.2 Notions of Discrepancy; A.3 Tractability Results; References; Index
Includes bibliographical references and index.
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.
Computer mathematics.
Economics, Mathematical .
Computational Mathematics and Numerical Analysis.
Quantitative Finance.
Lecture Notes in Computational Science and Engineering