Introduction To Quasi Monte Carlo Integration And Applications
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Introduction To Quasi Monte Carlo Integration And Applications
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Author : Gunther Leobacher
language : en
Publisher: Springer
Release Date : 2014-09-12
Introduction To Quasi Monte Carlo Integration And Applications written by Gunther Leobacher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-12 with Mathematics categories.
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.
Contributions To The Theory Of Monte Carlo And Quasi Monte Carlo Methods
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Author : Giray Okten
language : en
Publisher: Universal-Publishers
Release Date : 1999
Contributions To The Theory Of Monte Carlo And Quasi Monte Carlo Methods written by Giray Okten and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in "high" dimensional problems. Second, there is not a practical way to measure the error of a quasi-Monte Carlo simulation. Finally, unlike Monte Carlo methods, there is a scarcity of error reduction techniques for these methods. In this dissertation, we attempt to provide remedies for the disadvantages of quasi-Monte Carlo methods mentioned above. In the first part of the dissertation, a hybrid-Monte Carlo sequence designed to obtain error reduction in high dimensions is studied. Probabilistic results on the discrepancy of this sequence as well as results obtained by applying the sequence to problems from numerical integration and mathematical finance are presented. In the second part of the dissertation, a new hybrid-Monte Carlo method is introduced, in an attempt to obtain a practical statistical error analysis using low-discrepancy sequences. It is applied to problems from mathematical finance and particle transport theory to compare its effectiveness with the conventional methods. In the last part of the dissertation, a generalized quasi-Monte Carlo integration rule is introduced. A Koksma-Hlawka type inequality for the rule is proved, using a new concept for the variation of a function. As a consequence of the rule, error reduction techniques and in particular an "importance sampling" type statement are derived. Problems from different disciplines are used as practical tests for our methods. The numerical results obtained in favor of the methods suggest the practical advantages that can be realized by their use in a wide variety of applications.
Uniform Distribution And Quasi Monte Carlo Methods
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Author : Peter Kritzer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-08-19
Uniform Distribution And Quasi Monte Carlo Methods written by Peter Kritzer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-19 with Mathematics categories.
This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number theoretic point constructions, uniform distribution theory, and quasi-Monte Carlo methods. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules enjoy increasing popularity, with many fruitful applications in mathematical practice, as for example in finance, computer graphics, and biology. The goal of this book is to give an overview of recent developments in uniform distribution theory, quasi-Monte Carlo methods, and their applications, presented by leading experts in these vivid fields of research.
Digital Nets And Sequences
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Author : Josef Dick
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-09
Digital Nets And Sequences written by Josef Dick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-09 with Computers categories.
Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.
Monte Carlo And Quasi Monte Carlo Sampling
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Author : Christiane Lemieux
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Monte Carlo And Quasi Monte Carlo Sampling written by Christiane Lemieux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.
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.
Quasi Monte Carlo Methods In Finance
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Author : Mario Rometsch
language : en
Publisher: Diplomica Verlag
Release Date : 2008
Quasi Monte Carlo Methods In Finance written by Mario Rometsch and has been published by Diplomica Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Asset allocation categories.
Portfolio optimization is a widely studied problem in finance dating back to the work of Merton from the 1960s. While many approaches rely on dynamic programming, some recent contributions use martingale techniques to determine the optimal portfolio allocation. Using the latter approach, we follow a journal article from 2003 and show how optimal portfolio weights can be represented in terms of conditional expectations of the state variables and their Malliavin derivatives. In contrast to other approaches, where Monte Carlo methods are used to compute the weights, here the simulation is carried out using Quasi-Monte Carlo methods in order to improve the efficiency. Despite some previous work on Quasi-Monte Carlo simulation of stochastic differential equations, we find them to dominate plain Monte Carlo methods. However, the theoretical optimal order of convergence is not achieved. With the help of some recent results concerning Monte-Carlo error estimation and backed by some computer experiments on a simple model with explicit solution, we provide a first guess, what could be a way around this difficulties. The book is organized as follows. In the first chapter we provide some general introduction to Quasi-Monte Carlo methods and show at hand of a simple example how these methods can be used to accelerate the plain Monte Carlo sampling approach. In the second part we provide a thourough introduction to Malliavin Calculus and derive some important calculation rules that will be necessary in the third chapter. Right there we will focus on portfolio optimization and and follow a recent journal article of Detemple, Garcia and Rindisbacher from there rather general market model to the optimal portfolio formula. Finally, in the last part we will implement this optimal portfolio by means of a simple model with explicit solution where we find that also their the Quasi-Monte Carlo approach dominates the Monte Carlo method in terms of efficiency and accuracy.
Monte Carlo And Quasi Monte Carlo Methods
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Author : Art B. Owen
language : en
Publisher: Springer
Release Date : 2018-07-03
Monte Carlo And Quasi Monte Carlo Methods written by Art B. Owen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Computers categories.
This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.
Uniform Distribution And Quasi Monte Carlo Methods
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Author : Peter Kritzer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-06-23
Uniform Distribution And Quasi Monte Carlo Methods written by Peter Kritzer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-23 with Mathematics categories.
This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number theoretic point constructions, uniform distribution theory, and quasi-Monte Carlo methods. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules enjoy increasing popularity, with many fruitful applications in mathematical practice, as for example in finance, computer graphics, and biology. The goal of this book is to give an overview of recent developments in uniform distribution theory, quasi-Monte Carlo methods, and their applications, presented by leading experts in these vivid fields of research.
Monte Carlo And Quasi Monte Carlo Methods 1996
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Author : Harald Niederreiter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Monte Carlo And Quasi Monte Carlo Methods 1996 written by Harald Niederreiter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. This volume contains the refereed proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the University of Salzburg (Austria) from July 9--12, 1996. The conference was a forum for recent progress in the theory and the applications of these methods. The topics covered in this volume range from theoretical issues in Monte Carlo and simulation methods, low-discrepancy point sets and sequences, lattice rules, and pseudorandom number generation to applications such as numerical integration, numerical linear algebra, integral equations, binary search, global optimization, computational physics, mathematical finance, and computer graphics. These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods.
Monte Carlo And Quasi Monte Carlo Methods 2002
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Author : Harald Niederreiter
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Monte Carlo And Quasi Monte Carlo Methods 2002 written by Harald Niederreiter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
This book represents the refereed proceedings of the Fifth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the National University of Singapore in the year 2002. An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, computational complexity, finance, and other applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings also include carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active area.