Handbook of Monte Carlo Methods

Author: Dirk P. Kroese
Publisher: John Wiley & Sons
ISBN: 1118014952
Release Date: 2013-06-06
Genre: Mathematics

A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.

Handbook of Monte Carlo Methods

Author: Dirk P. Kroese
Publisher: John Wiley & Sons
ISBN: 9781118014943
Release Date: 2011-03-29
Genre: Mathematics

A comprehensive overview of Monte Carlo simulation that exploresthe latest topics, techniques, and real-world applications More and more of today’s numerical problems found inengineering and finance are solved through Monte Carlo methods. Theheightened popularity of these methods and their continuingdevelopment makes it important for researchers to have acomprehensive understanding of the Monte Carlo approach.Handbook of Monte Carlo Methods provides the theory,algorithms, and applications that helps provide a thoroughunderstanding of the emerging dynamics of this rapidly-growingfield. The authors begin with a discussion of fundamentals such as howto generate random numbers on a computer. Subsequent chaptersdiscuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as theMetropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation dataincluding the delta method, steady-state estimation, and kerneldensity estimation Variance reduction, including importance sampling, latinhypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kerneldensity estimation, quasi Monte Carlo, particle systems, andrandomized optimization The presented theoretical concepts are illustrated with workedexamples that use MATLAB®, a related Web sitehouses the MATLAB® code, allowing readers to workhands-on with the material and also features the author's ownlecture notes on Monte Carlo methods. Detailed appendices providebackground material on probability theory, stochastic processes,and mathematical statistics as well as the key optimizationconcepts and techniques that are relevant to Monte Carlosimulation. Handbook of Monte Carlo Methods is an excellent referencefor applied statisticians and practitioners working in the fieldsof engineering and finance who use or would like to learn how touse Monte Carlo in their research. It is also a suitable supplementfor courses on Monte Carlo methods and computational statistics atthe upper-undergraduate and graduate levels.

Handbook in Monte Carlo Simulation

Author: Paolo Brandimarte
Publisher: John Wiley & Sons
ISBN: 9781118593646
Release Date: 2014-06-17
Genre: Business & Economics

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.

Handbook of Markov Chain Monte Carlo

Author: Steve Brooks
Publisher: CRC Press
ISBN: 9781420079425
Release Date: 2011-05-10
Genre: Mathematics

Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as fisheries science and economics. The wide-ranging practical importance of MCMC has sparked an expansive and deep investigation into fundamental Markov chain theory. The Handbook of Markov Chain Monte Carlo provides a reference for the broad audience of developers and users of MCMC methodology interested in keeping up with cutting-edge theory and applications. The first half of the book covers MCMC foundations, methodology, and algorithms. The second half considers the use of MCMC in a variety of practical applications including in educational research, astrophysics, brain imaging, ecology, and sociology. The in-depth introductory section of the book allows graduate students and practicing scientists new to MCMC to become thoroughly acquainted with the basic theory, algorithms, and applications. The book supplies detailed examples and case studies of realistic scientific problems presenting the diversity of methods used by the wide-ranging MCMC community. Those familiar with MCMC methods will find this book a useful refresher of current theory and recent developments.

Mathematik und Technologie

Author: Christiane Rousseau
Publisher: Springer-Verlag
ISBN: 9783642300929
Release Date: 2012-07-30
Genre: Mathematics

Zusammen mit der Abstraktion ist die Mathematik das entscheidende Werkzeug für technologische Innovationen. Das Buch bietet eine Einführung in zahlreiche Anwendungen der Mathematik auf dem Gebiet der Technologie. Meist werden moderne Anwendungen dargestellt, die heute zum Alltag gehören. Die mathematischen Grundlagen für technologische Anwendungen sind dabei relativ elementar, was die Leistungsstärke der mathematischen Modellbildung und der mathematischen Hilfsmittel beweist. Mit zahlreichen originellen Übungen am Ende eines jeden Kapitels.

Handbook of Computational Finance

Author: Jin-Chuan Duan
Publisher: Springer Science & Business Media
ISBN: 3642172547
Release Date: 2011-10-25
Genre: Business & Economics

Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.

Handbook on Analyzing Human Genetic Data

Author: Shili Lin
Publisher: Springer Science & Business Media
ISBN: 9783540692645
Release Date: 2009-10-13
Genre: Medical

This handbook offers guidance on selections of appropriate computational methods and software packages for specific genetic problems. Coverage strikes a balance between methodological expositions and practical guidelines for software selections. Wherever possible, comparisons among competing methods and software are made to highlight the relative advantages and disadvantage of the approaches.

The Handbook of Convertible Bonds

Author: Jan De Spiegeleer
Publisher: John Wiley & Sons
ISBN: 9781119978060
Release Date: 2011-07-07
Genre: Business & Economics

This is a complete guide to the pricing and risk management of convertible bond portfolios. Convertible bonds can be complex because they have both equity and debt like features and new market entrants will usually find that they have either a knowledge of fixed income mathematics or of equity derivatives and therefore have no idea how to incorporate credit and equity together into their existing pricing tools. Part I of the book covers the impact that the 2008 credit crunch has had on the markets, it then shows how to build up a convertible bond and introduces the reader to the traditional convertible vocabulary of yield to put, premium, conversion ratio, delta, gamma, vega and parity. The market of stock borrowing and lending will also be covered in detail. Using an intuitive approach based on the Jensen inequality, the authors will also show the advantages of using a hybrid to add value - pre 2008, many investors labelled convertible bonds as 'investing with no downside', there are of course plenty of 2008 examples to prove that they were wrong. The authors then go onto give a complete explanation of the different features that can be embedded in convertible bond. Part II shows readers how to price convertibles. It covers the different parameters used in valuation models: credit spreads, volatility, interest rates and borrow fees and Maturity. Part III covers investment strategies for equity, fixed income and hedge fund investors and includes dynamic hedging and convertible arbitrage. Part IV explains the all important risk management part of the process in detail. This is a highly practical book, all products priced are real world examples and numerical examples are not limited to hypothetical convertibles. It is a must read for anyone wanting to safely get into this highly liquid, high return market.

Computational Statistics Handbook with MATLAB Second Edition

Author: Wendy L. Martinez
Publisher: CRC Press
ISBN: 9781420010862
Release Date: 2007-12-20
Genre: Mathematics

As with the bestselling first edition, Computational Statistics Handbook with MATLAB®, Second Edition covers some of the most commonly used contemporary techniques in computational statistics. With a strong, practical focus on implementing the methods, the authors include algorithmic descriptions of the procedures as well as examples that illustrate the use of the algorithms in data analysis. Updated for MATLAB® R2007a and the Statistics Toolbox, Version 6.0, this edition incorporates many additional computational statistics topics. New to the Second Edition • New functions for multivariate normal and multivariate t distributions • Updated information on the new MATLAB functionality for univariate and bivariate histograms, glyphs, and parallel coordinate plots • New content on independent component analysis, nonlinear dimensionality reduction, and multidimensional scaling • New topics on linear classifiers, quadratic classifiers, and voting methods, such as bagging, boosting, and random forests • More methods for unsupervised learning, including model-based clustering and techniques for assessing the results of clustering • A new chapter on parametric models that covers spline regression models, logistic regression, and generalized linear models • Expanded information on smoothers, such as bin smoothing, running mean and line smoothers, and smoothing splines With numerous problems and suggestions for further reading, this accessible text facilitates an understanding of computational statistics concepts and how they are employed in data analysis.

Handbook of Computational and Numerical Methods in Finance

Author: Svetlozar T. Rachev
Publisher: Springer Science & Business Media
ISBN: 9780817681807
Release Date: 2011-06-28
Genre: Mathematics

The subject of numerical methods in finance has recently emerged as a new discipline at the intersection of probability theory, finance, and numerical analysis. The methods employed bridge the gap between financial theory and computational practice, and provide solutions for complex problems that are difficult to solve by traditional analytical methods. Although numerical methods in finance have been studied intensively in recent years, many theoretical and practical financial aspects have yet to be explored. This volume presents current research and survey articles focusing on various numerical methods in finance. The book is designed for the academic community and will also serve professional investors.

Handbook of Computational Statistics

Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 9783642215513
Release Date: 2012-07-06
Genre: Computers

The Handbook of Computational Statistics - Concepts and Methods (second edition) is a revision of the first edition published in 2004, and contains additional comments and updated information on the existing chapters, as well as three new chapters addressing recent work in the field of computational statistics. This new edition is divided into 4 parts in the same way as the first edition. It begins with "How Computational Statistics became the backbone of modern data science" (Ch.1): an overview of the field of Computational Statistics, how it emerged as a separate discipline, and how its own development mirrored that of hardware and software, including a discussion of current active research. The second part (Chs. 2 - 15) presents several topics in the supporting field of statistical computing. Emphasis is placed on the need for fast and accurate numerical algorithms, and some of the basic methodologies for transformation, database handling, high-dimensional data and graphics treatment are discussed. The third part (Chs. 16 - 33) focuses on statistical methodology. Special attention is given to smoothing, iterative procedures, simulation and visualization of multivariate data. Lastly, a set of selected applications (Chs. 34 - 38) like Bioinformatics, Medical Imaging, Finance, Econometrics and Network Intrusion Detection highlight the usefulness of computational statistics in real-world applications.

Monte Carlo

Author: George Fishman
Publisher: Springer Science & Business Media
ISBN: 038794527X
Release Date: 1996-04-25
Genre: Business & Economics

Apart from a thorough exploration of all the important concepts, this volume includes over 75 algorithms, ready for putting into practice. The book also contains numerous hands-on implementations of selected algorithms to demonstrate applications in realistic settings. Readers are assumed to have a sound understanding of calculus, introductory matrix analysis, and intermediate statistics, but otherwise the book is self-contained. Suitable for graduates and undergraduates in mathematics and engineering, in particular operations research, statistics, and computer science.

Engineering Design Reliability Handbook

Author: Efstratios Nikolaidis
Publisher: CRC Press
ISBN: 9780203483930
Release Date: 2004-12-22
Genre: Technology & Engineering

Researchers in the engineering industry and academia are making important advances on reliability-based design and modeling of uncertainty when data is limited. Non deterministic approaches have enabled industries to save billions by reducing design and warranty costs and by improving quality. Considering the lack of comprehensive and definitive presentations on the subject, Engineering Design Reliability Handbook is a valuable addition to the reliability literature. It presents the perspectives of experts from the industry, national labs, and academia on non-deterministic approaches including probabilistic, interval and fuzzy sets-based methods, generalized information theory, Dempster-Shaffer evidence theory, and robust reliability. It also presents recent advances in all important fields of reliability design including modeling of uncertainty, reliability assessment of both static and dynamic components and systems, design decision making in the face of uncertainty, and reliability validation. The editors and the authors also discuss documented success stories and quantify the benefits of these approaches. With contributions from a team of respected international authors and the guidance of esteemed editors, this handbook is a distinctive addition to the acclaimed line of handbooks from CRC Press.

Handbook of Spatial Statistics

Author: Alan E. Gelfand
Publisher: CRC Press
ISBN: 1420072889
Release Date: 2010-03-19
Genre: Mathematics

Assembling a collection of very prominent researchers in the field, the Handbook of Spatial Statistics presents a comprehensive treatment of both classical and state-of-the-art aspects of this maturing area. It takes a unified, integrated approach to the material, providing cross-references among chapters. The handbook begins with a historical introduction detailing the evolution of the field. It then focuses on the three main branches of spatial statistics: continuous spatial variation (point referenced data); discrete spatial variation, including lattice and areal unit data; and spatial point patterns. The book also contains a section on space–time work as well as a section on important topics that build upon earlier chapters. By collecting the major work in the field in one source, along with including an extensive bibliography, this handbook will assist future research efforts. It deftly balances theory and application, strongly emphasizes modeling, and introduces many real data analysis examples.