Introduction to Quasi-Monte Carlo Integration and Applications

Buch | Softcover
XII, 195 Seiten
2014 | 2014
Springer International Publishing (Verlag)
978-3-319-03424-9 (ISBN)

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Introduction to Quasi-Monte Carlo Integration and Applications - Gunther Leobacher, Friedrich Pillichshammer
69,54 inkl. MwSt
This book introduces the basic concepts of quasi-Monte Carlo methods for numerical integration and the theory behind them. It also presents methods currently used in research and discusses practical applications with an emphasis on finance-related problems.

This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed explanations comprises, for example, lattice rules, digital nets and sequences and discrepancy theory. It also presents methods currently used in research and discusses practical applications with an emphasis on finance-related problems. Each chapter closes with suggestions for further reading and with exercises which help students to arrive at a deeper understanding of the material presented.

The book is based on a one-semester, two-hour undergraduate course and is well-suited for readers with a basic grasp of algebra, calculus, linear algebra and basic probability theory. It provides an accessible introduction for undergraduate students in mathematics or computer science.

Gunther Leobacher is assistant professor at the Institute of Financial Mathematics at the Johannes Kepler University Linz. Friedrich Pillichshammer is associate professor at the Institute of Financial Mathematics at the Johannes Kepler University Linz.

Preface.- Notation.- 1 Introduction.- 2 Uniform Distribution Modulo One.- 3 QMC Integration in Reproducing Kernel Hilbert Spaces.- 4 Lattice Point Sets.- 5 (t, m, s)-nets and (t, s)-Sequences.- 6 A Short Discussion of the Discrepancy Bounds.- 7 Foundations of Financial Mathematics.- 8 Monte Carlo and Quasi-Monte Carlo Simulation.- Bibliography.- Index.

"The book under review is based on a one-semester undergraduate course and suited for readers with a basic knowledge in linear algebra, finite fields, calculus and elementary probability theory. The authors give a concise and well-written introduction to multivariate integration by Quasi-Monte Carlo (QMC) techniques and applications to mathematical finance. ... Every chapter contains interesting exercise problems and useful hints for further reading of related literature." (Robert F. Tichy, Mathematical Reviews, June, 2015)

Erscheint lt. Verlag 2.10.2014
Reihe/Serie Compact Textbooks in Mathematics
Zusatzinfo XII, 195 p. 21 illus., 16 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 310 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Wirtschaft Betriebswirtschaft / Management
Schlagworte digital nets • discrepancy • lattice rules • Monte-Carlo-Methode • Numerical Integration • Quantitative Finance • quasi-Monte Carlo • Uniform distribution
ISBN-10 3-319-03424-3 / 3319034243
ISBN-13 978-3-319-03424-9 / 9783319034249
Zustand Neuware
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