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Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance
Markus Holtz
出版Springer Science & Business Media, 2010-10-22
主題Mathematics / Counting & NumerationMathematics / AppliedMathematics / Numerical AnalysisMathematics / Probability & Statistics / Stochastic ProcessesBusiness & Economics / Accounting / General
ISBN36421600429783642160042
URLhttp://books.google.com.hk/books?id=XOfMm-4ZM9AC&hl=&source=gbs_api
EBookSAMPLE
註釋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.