Essentials of Monte Carlo Simulation

Statistical Methods for Building Simulation Models

Author: Nick T. Thomopoulos

Publisher: Springer Science & Business Media

ISBN: 1461460220

Category: Mathematics

Page: 174

View: 6836

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Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. The theories presented in this text deal with systems that are too complex to solve analytically. As a result, readers are given a system of interest and constructs using computer code, as well as algorithmic models to emulate how the system works internally. After the models are run several times, in a random sample way, the data for each output variable(s) of interest is analyzed by ordinary statistical methods. This book features 11 comprehensive chapters, and discusses such key topics as random number generators, multivariate random variates, and continuous random variates. Over 100 numerical examples are presented as part of the appendix to illustrate useful real world applications. The text also contains an easy to read presentation with minimal use of difficult mathematical concepts. Very little has been published in the area of computer Monte Carlo simulation methods, and this book will appeal to students and researchers in the fields of Mathematics and Statistics.

Monte Carlo Methods in Financial Engineering

Author: Paul Glasserman

Publisher: Springer Science & Business Media

ISBN: 0387216170

Category: Mathematics

Page: 596

View: 8476

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From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis

Monte Carlo Simulation and Finance

Author: Don L. McLeish

Publisher: John Wiley & Sons

ISBN: 1118160940

Category: Business & Economics

Page: 387

View: 3147

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Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.

A Guide to Monte Carlo Simulations in Statistical Physics

Author: David P. Landau,Kurt Binder

Publisher: Cambridge University Press

ISBN: 1316062635

Category: Science

Page: N.A

View: 4452

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Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This fourth edition contains extensive new material describing numerous powerful algorithms not covered in previous editions, in some cases representing new developments that have only recently appeared. Older methodologies whose impact was previously unclear or unappreciated are also introduced, in addition to many small revisions that bring the text and cited literature up to date. This edition also introduces the use of petascale computing facilities in the Monte Carlo arena. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory.

Monte Carlo Simulation

Author: Christopher Z. Mooney

Publisher: SAGE

ISBN: 9780803959439

Category: Education

Page: 103

View: 5432

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The author explains the logic behind the method and demonstrates its uses for social and behavioral research in: conducting inference using statistics with only weak mathematical theory; testing null hypotheses under a variety of plausible conditions; assessing the robustness of parametric inference to violations of its assumptions; assessing the quality of inferential methods; and comparing the properties of two or more estimators. In addition, Christopher Z Mooney carefully demonstrates how to prepare computer algorithms using GAUSS code and uses several research examples to demonstrate these principles. This volume will enable researchers to execute Monte Carlo Simulation effectively and to interpret the estimated sampling distribution generated from its use.

Monte Carlo Methods for Particle Transport

Author: Alireza Haghighat

Publisher: CRC Press

ISBN: 1466592540

Category: Mathematics

Page: 272

View: 7451

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The Monte Carlo method has become the de facto standard in radiation transport. Although powerful, if not understood and used appropriately, the method can give misleading results. Monte Carlo Methods for Particle Transport teaches appropriate use of the Monte Carlo method, explaining the method’s fundamental concepts as well as its limitations. Concise yet comprehensive, this well-organized text: Introduces the particle importance equation and its use for variance reduction Describes general and particle-transport-specific variance reduction techniques Presents particle transport eigenvalue issues and methodologies to address these issues Explores advanced formulations based on the author’s research activities Discusses parallel processing concepts and factors affecting parallel performance Featuring illustrative examples, mathematical derivations, computer algorithms, and homework problems, Monte Carlo Methods for Particle Transport provides nuclear engineers and scientists with a practical guide to the application of the Monte Carlo method.

Exploring Monte Carlo Methods

Author: William L. Dunn,J. Kenneth Shultis

Publisher: Elsevier

ISBN: 9780080930619

Category: Mathematics

Page: 398

View: 9525

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Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon’s needle problem" provides a unifying theme as it is repeatedly used to illustrate many features of Monte Carlo methods. This book provides the basic detail necessary to learn how to apply Monte Carlo methods and thus should be useful as a text book for undergraduate or graduate courses in numerical methods. It is written so that interested readers with only an understanding of calculus and differential equations can learn Monte Carlo on their own. Coverage of topics such as variance reduction, pseudo-random number generation, Markov chain Monte Carlo, inverse Monte Carlo, and linear operator equations will make the book useful even to experienced Monte Carlo practitioners. Provides a concise treatment of generic Monte Carlo methods Proofs for each chapter Appendixes include Certain mathematical functions; Bose Einstein functions, Fermi Dirac functions, Watson functions

Monte Carlo Simulation and Resampling Methods for Social Science

Author: Thomas M. Carsey,Jeffrey J. Harden

Publisher: SAGE Publications

ISBN: 1483324923

Category: Social Science

Page: 304

View: 1094

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Taking the topics of a quantitative methodology course and illustrating them through Monte Carlo simulation, Monte Carlo Simulation and Resampling Methods for Social Science, by Thomas M. Carsey and Jeffrey J. Harden, examines abstract principles, such as bias, efficiency, and measures of uncertainty in an intuitive, visual way. Instead of thinking in the abstract about what would happen to a particular estimator "in repeated samples," the book uses simulation to actually create those repeated samples and summarize the results. The book includes basic examples appropriate for readers learning the material for the first time, as well as more advanced examples that a researcher might use to evaluate an estimator he or she was using in an actual research project. The book also covers a wide range of topics related to Monte Carlo simulation, such as resampling methods, simulations of substantive theory, simulation of quantities of interest (QI) from model results, and cross-validation. Complete R code from all examples is provided so readers can replicate every analysis presented using R.

Stochastic Simulation and Monte Carlo Methods

Mathematical Foundations of Stochastic Simulation

Author: Carl Graham,Denis Talay

Publisher: Springer Science & Business Media

ISBN: 3642393632

Category: Mathematics

Page: 260

View: 9601

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In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.

Random Number Generation and Monte Carlo Methods

Author: James E. Gentle

Publisher: Springer Science & Business Media

ISBN: 147572960X

Category: Computers

Page: 247

View: 5543

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Monte Carlo simulation has become one of the most important tools in all fields of science. This book surveys the basic techniques and principles of the subject, as well as general techniques useful in more complicated models and in novel settings. The emphasis throughout is on practical methods that work well in current computing environments.

Monte Carlo Simulation with Applications to Finance

Author: Hui Wang

Publisher: CRC Press

ISBN: 1439858241

Category: Business & Economics

Page: 292

View: 1962

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Developed from the author’s course on Monte Carlo simulation at Brown University, Monte Carlo Simulation with Applications to Finance provides a self-contained introduction to Monte Carlo methods in financial engineering. It is suitable for advanced undergraduate and graduate students taking a one-semester course or for practitioners in the financial industry. The author first presents the necessary mathematical tools for simulation, arbitrary free option pricing, and the basic implementation of Monte Carlo schemes. He then describes variance reduction techniques, including control variates, stratification, conditioning, importance sampling, and cross-entropy. The text concludes with stochastic calculus and the simulation of diffusion processes. Only requiring some familiarity with probability and statistics, the book keeps much of the mathematics at an informal level and avoids technical measure-theoretic jargon to provide a practical understanding of the basics. It includes a large number of examples as well as MATLAB® coding exercises that are designed in a progressive manner so that no prior experience with MATLAB is needed.

Introductory Econometrics

Using Monte Carlo Simulation with Microsoft Excel

Author: Humberto Barreto,Frank Howland

Publisher: Cambridge University Press

ISBN: 9780521843195

Category: Business & Economics

Page: 774

View: 2141

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This highly accessible and innovative text with supporting web site uses Excel (R) to teach the core concepts of econometrics without advanced mathematics. It enables students to use Monte Carlo simulations in order to understand the data generating process and sampling distribution. Intelligent repetition of concrete examples effectively conveys the properties of the ordinary least squares (OLS) estimator and the nature of heteroskedasticity and autocorrelation. Coverage includes omitted variables, binary response models, basic time series, and simultaneous equations. The authors teach students how to construct their own real-world data sets drawn from the internet, which they can analyze with Excel (R) or with other econometric software. The accompanying web site with text support can be found at www.wabash.edu/econometrics.

Handbook in Monte Carlo Simulation

Applications in Financial Engineering, Risk Management, and Economics

Author: Paolo Brandimarte

Publisher: John Wiley & Sons

ISBN: 1118594517

Category: Business & Economics

Page: 688

View: 4892

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An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.

Simulation and the Monte Carlo Method

Author: Reuven Y. Rubinstein,Dirk P. Kroese

Publisher: John Wiley & Sons

ISBN: 1118210522

Category: Mathematics

Page: 372

View: 3208

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This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo Variance reduction techniques such as the transform likelihood ratio method and the screening method The score function method for sensitivity analysis The stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization The cross-entropy method to rare events estimation and combinatorial optimization Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB programs. Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method.

Introducing Monte Carlo Methods with R

Author: Christian Robert,George Casella

Publisher: Springer Science & Business Media

ISBN: 1441915753

Category: Computers

Page: 284

View: 1798

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This book covers the main tools used in statistical simulation from a programmer’s point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison.

A Guide to Monte Carlo Simulations in Statistical Physics

Author: David P. Landau,Kurt Binder

Publisher: Cambridge University Press

ISBN: 1316062635

Category: Science

Page: N.A

View: 8005

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Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This fourth edition contains extensive new material describing numerous powerful algorithms not covered in previous editions, in some cases representing new developments that have only recently appeared. Older methodologies whose impact was previously unclear or unappreciated are also introduced, in addition to many small revisions that bring the text and cited literature up to date. This edition also introduces the use of petascale computing facilities in the Monte Carlo arena. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory.

Monte Carlo Simulation of Semiconductor Devices

Author: C. Moglestue

Publisher: Springer Science & Business Media

ISBN: 9401581339

Category: Computers

Page: 334

View: 4078

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Particle simulation of semiconductor devices is a rather new field which has started to catch the interest of the world's scientific community. It represents a time-continuous solution of Boltzmann's transport equation, or its quantum mechanical equivalent, and the field equation, without encountering the usual numerical problems associated with the direct solution. The technique is based on first physical principles by following in detail the transport histories of indi vidual particles and gives a profound insight into the physics of semiconductor devices. The method can be applied to devices of any geometrical complexity and material composition. It yields an accurate description of the device, which is not limited by the assumptions made behind the alternative drift diffusion and hydrodynamic models, which represent approximate solutions to the transport equation. While the development of the particle modelling technique has been hampered in the past by the cost of computer time, today this should not be held against using a method which gives a profound physical insight into individual devices and can be used to predict the properties of devices not yet manufactured. Employed in this way it can save the developer much time and large sums of money, both important considerations for the laboratory which wants to keep abreast of the field of device research. Applying it to al ready existing electronic components may lead to novel ideas for their improvement. The Monte Carlo particle simulation technique is applicable to microelectronic components of any arbitrary shape and complexity.

Monte Carlo Strategies in Scientific Computing

Author: Jun S. Liu

Publisher: Springer Science & Business Media

ISBN: 0387763716

Category: Mathematics

Page: 344

View: 4649

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This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.

Monte-Carlo Simulation-Based Statistical Modeling

Author: Ding-Geng (Din) Chen,John Dean Chen

Publisher: Springer

ISBN: 9811033072

Category: Medical

Page: 430

View: 2633

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This book brings together expert researchers engaged in Monte-Carlo simulation-based statistical modeling, offering them a forum to present and discuss recent issues in methodological development as well as public health applications. It is divided into three parts, with the first providing an overview of Monte-Carlo techniques, the second focusing on missing data Monte-Carlo methods, and the third addressing Bayesian and general statistical modeling using Monte-Carlo simulations. The data and computer programs used here will also be made publicly available, allowing readers to replicate the model development and data analysis presented in each chapter, and to readily apply them in their own research. Featuring highly topical content, the book has the potential to impact model development and data analyses across a wide spectrum of fields, and to spark further research in this direction.