# Monte Carlo and Quasi-Monte Carlo Sampling

## Benefits

• Many books have been written on the Monte Carlo method and its applications, especially in finance, stochastic simulation, and quasi-Monte Carlo methods

• Presents all these topics together in one place in a unified way, by continuously using the interplay between integration and simulation

• Reader will be able to apply random sampling to a wide range of problems and understand how to replace it by highly-uniform sampling

Book

Part of the Springer Series in Statistics book series (SSS)

1. Front Matter
Pages 1-12
2. Christiane Lemieux
Pages 1-39
3. Christiane Lemieux
Pages 1-16
4. Christiane Lemieux
Pages 1-30
5. Christiane Lemieux
Pages 1-52
6. Christiane Lemieux
Pages 1-61
7. Christiane Lemieux
Pages 1-46
8. Christiane Lemieux
Pages 1-54
9. Christiane Lemieux
Pages 1-33
10. Back Matter
Pages 1-38

### Introduction

Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute.

This book presents essential tools for using quasi–Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi–random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi–Monte Carlo counterpart.

The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi–Monte Carlo methods and researchers interested in an up-to-date guide to these methods.

Christiane Lemieux is an Associate Professor and the Associate Chair for Actuarial Science in the Department of Statistics and Actuarial Science at the University of Waterloo in Canada. She is an Associate of the Society of Actuaries and was the winner of a "Young Researcher Award in Information-Based Complexity" in 2004.

### Keywords

ANOVA Monte Carlo Monte Carlo method STATISTICA Variance integration quasi-Monte Carlo simulation

#### Authors and affiliations

There are no affiliations available

Christiane Lemieux is an Associate Professor and the Associate Chair for Actuarial Science in the Department of Statistics and Actuarial Science at the University of Waterloo in Canada. She is an Associate of the Society of Actuaries and was the winner of a “Young Researcher Award in Information-Based Complexity” in 2004.

### Bibliographic information

• Book Title Monte Carlo and Quasi-Monte Carlo Sampling
• Authors Christiane Lemieux
• Series Title Springer Series in Statistics
• DOI https://doi.org/10.1007/978-0-387-78165-5
• Copyright Information Springer-Verlag New York 2009
• Publisher Name Springer, New York, NY
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-0-387-78164-8
• Softcover ISBN 978-1-4419-2676-0
• eBook ISBN 978-0-387-78165-5
• Series ISSN 0172-7397
• Edition Number 1
• Number of Pages XIV, 373
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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