Download or read book Digital Nets and Sequences written by Josef Dick and published by Cambridge University Press. This book was released on 2010-09-09 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Digital Nets and Sequences written by Josef Dick and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Digital Nets and Sequences written by Josef Dick and published by . This book was released on 2014-05-14 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to contemporary quasi Monte Carlo methods, digital nets and sequences, and discrepancy theory. Includes many exercises, examples and illustrations.
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2008 written by Pierre L' Ecuyer and published by Springer Science & Business Media. This book was released on 2010-01-14 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Eighth International Conference on Monte Carlo (MC)and Quasi-Monte Carlo (QMC) Methods in Scientific Computing, held in Montreal (Canada) in July 2008. It covers the latest theoretical developments as well as important applications of these methods in different areas. It contains two tutorials, eight invited articles, and 32 carefully selected articles based on the 135 contributed presentations made at the conference. This conference is a major event in Monte Carlo methods and is the premiere event for quasi-Monte Carlo and its combination with Monte Carlo. This series of proceedings volumes is the primary outlet for quasi-Monte Carlo research.
Download or read book Monte Carlo and Quasi Monte Carlo Sampling written by Christiane Lemieux and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Random and Quasi Random Point Sets written by Peter Hellekalek and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of survey papers on recent developments in the fields of quasi-Monte Carlo methods and uniform random number generation. We will cover a broad spectrum of questions, from advanced metric number theory to pricing financial derivatives. The Monte Carlo method is one of the most important tools of system modeling. Deterministic algorithms, so-called uniform random number gen erators, are used to produce the input for the model systems on computers. Such generators are assessed by theoretical ("a priori") and by empirical tests. In the a priori analysis, we study figures of merit that measure the uniformity of certain high-dimensional "random" point sets. The degree of uniformity is strongly related to the degree of correlations within the random numbers. The quasi-Monte Carlo approach aims at improving the rate of conver gence in the Monte Carlo method by number-theoretic techniques. It yields deterministic bounds for the approximation error. The main mathematical tool here are so-called low-discrepancy sequences. These "quasi-random" points are produced by deterministic algorithms and should be as "super" uniformly distributed as possible. Hence, both in uniform random number generation and in quasi-Monte Carlo methods, we study the uniformity of deterministically generated point sets in high dimensions. By a (common) abuse oflanguage, one speaks of random and quasi-random point sets. The central questions treated in this book are (i) how to generate, (ii) how to analyze, and (iii) how to apply such high-dimensional point sets.
Download or read book Sequences Discrepancies and Applications written by Michael Drmota and published by Springer. This book was released on 2006-11-14 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2000 written by Kai-Tai Fang and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Hong Kong Baptist University in 2000. An important feature are invited surveys of the state-of-the-art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also 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 field.
Download or read book Applied Algebra and Number Theory written by Gerhard Larcher and published by Cambridge University Press. This book was released on 2014-12-11 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harald Niederreiter's pioneering research in the field of applied algebra and number theory has led to important and substantial breakthroughs in many areas. This collection of survey articles has been authored by close colleagues and leading experts to mark the occasion of his 70th birthday. The book provides a modern overview of different research areas, covering uniform distribution and quasi-Monte Carlo methods as well as finite fields and their applications, in particular, cryptography and pseudorandom number generation. Many results are published here for the first time. The book serves as a useful starting point for graduate students new to these areas or as a refresher for researchers wanting to follow recent trends.
Download or read book Discrepancy Theory written by Dmitriy Bilyk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-01-20 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2006 written by Alexander Keller and published by Springer Science & Business Media. This book was released on 2007-12-30 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm, Germany, in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications. They also provide information on current research in these very active areas.
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2002 written by Harald Niederreiter and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbooks in Operations Research and Management Science Simulation written by Shane G. Henderson and published by Elsevier. This book was released on 2006-09-02 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook is a collection of chapters on key issues in the design and analysis of computer simulation experiments on models of stochastic systems. The chapters are tightly focused and written by experts in each area. For the purpose of this volume “simulation refers to the analysis of stochastic processes through the generation of sample paths (realization) of the processes. Attention focuses on design and analysis issues and the goal of this volume is to survey the concepts, principles, tools and techniques that underlie the theory and practice of stochastic simulation design and analysis. Emphasis is placed on the ideas and methods that are likely to remain an intrinsic part of the foundation of the field for the foreseeable future. The chapters provide up-to-date references for both the simulation researcher and the advanced simulation user, but they do not constitute an introductory level ‘how to’ guide. Computer scientists, financial analysts, industrial engineers, management scientists, operations researchers and many other professionals use stochastic simulation to design, understand and improve communications, financial, manufacturing, logistics, and service systems. A theme that runs throughout these diverse applications is the need to evaluate system performance in the face of uncertainty, including uncertainty in user load, interest rates, demand for product, availability of goods, cost of transportation and equipment failures. * Tightly focused chapters written by experts * Surveys concepts, principles, tools, and techniques that underlie the theory and practice of stochastic simulation design and analysis * Provides an up-to-date reference for both simulation researchers and advanced simulation users
Download or read book Monte Carlo and Quasi Monte Carlo Methods written by Ronald Cools and published by Springer. This book was released on 2016-06-13 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. 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 and computer graphics.
Download or read book Quasi Monte Carlo Methods in Finance with Application to Optimal Asset Allocation written by Mario Rometsch and published by diplom.de. This book was released on 2014-04-11 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inhaltsangabe:Introduction: Portfolio optimization is a widely studied problem in finance. The common question is, how a small investor should invest his wealth in the market to attain certain goals, like a desired payoff or some insurance against unwished events. The starting point for the mathematical treatment of this is the work of Harry Markowitz in the 1950s. His idea was to set up a relation between the mean return of a portfolio and its variance. In his terminology, an efficient portfolio has minimal variance of return among others with the same mean rate of return. Furthermore, if linear combinations of efficient portfolios and a riskless asset are allowed, this leads to the market portfolio, so that a linear combination of the risk-free asset and the market portfolio dominates any other portfolio in the mean-variance sense. Later, this theory was extended resulting in the CAPM, or capital asset pricing model, which was independently introduced by Treynor, Sharpe, Lintner and Mossin in the 1960s. In this model, every risky asset has a mean rate of return that exceeds the risk-free rate by a specific risk premium, which depends on a certain attribute of the asset, namely its _. The so-called _ in turn is the covariance of the asset return normalized by the variance of the market portfolio. The problem of the CAPM is its static nature, investments are made once and then the state of the model changes. Due to this and other simplifications, this model was and is often not found to be realistic. An impact to this research field were the two papers of Robert Merton in 1969 and 1971. He applied the theory of Ito calculus and stochastic optimal control and solved the corresponding Hamilton-Jacobi-Bellman equation. For his multiperiod model, he assumed constant coefficients and an investor with power utility. Extending the mean-variance analysis, he found that a long-term investor would prefer a portfolio that includes hedging components to protect against fluctuations in the market. Again this approach was generalized by numerous researchers and results in the problem of solving a nonlinear partial differential equation. The next milestone in this series is the work by Cox and Huang from 1989, where they solve for Optimal Consumption and Portfolio Policies when Asset Prices Follow a Diffusion Process . They apply the martingale technique to get rid of the nonlinear PDE and rather solve a linear PDE. This, with several refinements, is [...]
Download or read book Implementing Models in Quantitative Finance Methods and Cases written by Gianluca Fusai and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.
Download or read book Parallel Computation written by Peter Zinterhof and published by Springer. This book was released on 2003-05-21 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Parallel Computation, ACPC'99, held in Salzburg, Austria in February 1999; the conference included special tracks on parallel numerics and on parallel computing in image processing, video processing, and multimedia. The volume presents 50 revised full papers selected from a total of 75 submissions. Also included are four invited papers and 15 posters. The papers are organized in topical sections on linear algebra, differential equations and interpolation, (Quasi-)Monte Carlo methods, numerical software, numerical applications, image segmentation and image understanding, motion estimation and block matching, video processing, wavelet techniques, satellite image processing, data structures, data partitioning, resource allocation and performance analysis, cluster computing, and simulation and applications.
