The Monte Carlo Methods

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Monte Carlo Methods

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Author : Adrian Barbu
language : en
Publisher: Springer Nature
Release Date : 2020-02-24

Monte Carlo Methods written by Adrian Barbu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-24 with Mathematics categories.

This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.

Essentials Of Monte Carlo Simulation

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Author : Nick T. Thomopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-19

Essentials Of Monte Carlo Simulation written by Nick T. Thomopoulos 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 2012-12-19 with Mathematics categories.

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.

Explorations In Monte Carlo Methods

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Author : Ronald W. Shonkwiler
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-11

Explorations In Monte Carlo Methods written by Ronald W. Shonkwiler 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 2009-08-11 with Mathematics categories.

Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics. The problem-oriented approach makes it ideal for an applied course in basic probability and for a more specialized course in Monte Carlo methods. Topics include probability distributions, counting combinatorial objects, simulated annealing, genetic algorithms, option pricing, gamblers ruin, statistical mechanics, sampling, and random number generation.

Monte Carlo Methods

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Author : Malvin H. Kalos
language : en
Publisher: John Wiley & Sons
Release Date : 2008-09-26

Monte Carlo Methods written by Malvin H. Kalos and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-26 with Science categories.

This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on that example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The detailed discussion of variance reduction includes Monte Carlo evaluation of finite-dimensional integrals. Special attention is given to importance sampling, partly because of its intrinsic interest in quadrature, partly because of its general usefulness in the solution of integral equations. One significant feature is that Monte Carlo Methods treats the "Metropolis algorithm" in the context of sampling methods, clearly distinguishing it from importance sampling. Physicists, chemists, statisticians, mathematicians, and computer scientists will find Monte Carlo Methods a complete and stimulating introduction.

Monte Carlo

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Author : George Fishman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Monte Carlo written by George Fishman 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 2013-03-09 with Mathematics categories.

This book provides an introduction to the Monte Carlo method suitable for a one-or two-semester course for graduate and advanced undergraduate students in the mathematical and engineering sciences. It also can serve as a reference for the professional analyst. In the past, my inability to provide students with a single source book on this topic for class and for later professional reference had left me repeatedly frustrated, and eventually motivated me to write this book. In addition to focused accounts of major topics, the book has two unifying themes: One concerns the effective use of information and the other concerns error control and reduction. The book describes how to incorporate information about a problem into a sampling plan in a way that reduces the cost of estimating its solution to within a specified error bound. Although exploiting special structures to reduce cost long has been a hallmark of the Monte Carlo method, the propen sity of users of the method to discard useful information because it does not fit traditional textbook models repeatedly has impressed me. The present account aims at reducing the impediments to integrating this information. Errors, both statistical and computational, abound in every Monte Carlo sam pling experiment, and a considerable methodology exists for controlling them.

Monte Carlo Methods In Finance

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Author : Peter Jäckel
language : de
Publisher: John Wiley & Sons
Release Date : 2002-04-03

Monte Carlo Methods In Finance written by Peter Jäckel and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-03 with Business & Economics categories.

Dieses Buch ist ein handlicher und praktischer Leitfaden zur Monte Carlo Simulation (MCS). Er gibt eine Einführung in Standardmethoden und fortgeschrittene Verfahren, um die zunehmende Komplexität derivativer Portfolios besser zu erfassen. Das hier behandelte Spektrum von MCS-Anwendungen reicht von der Preisbestimmung komplexerer Derivate, z.B. von amerikanischen und asiatischen Optionen, bis hin zur Messung des Value at Risk und zur Modellierung komplexer Marktdynamik. Anhand einer Vielzahl praktischer Beispiele wird erläutert, wie man Monte Carlo Methoden einsetzt. Dabei gehen die Autoren zunächst auf die Grundlagen und danach auf fortgeschrittene Techniken ein. Darüber hinaus geben sie nützliche Tipps und Hinweise für das Entwickeln und Arbeiten mit MCS-Methoden. Die Autoren sind Experten auf dem Gebiet der Monte Carlo Simulation und verfügen über langjährige Erfahrung im Umgang mit MCS-Methoden. Die Begleit-CD enthält Excel Muster Spreadsheets sowie VBA und C++ Code Snippets, die der Leser installieren und so mit den im Buch beschriebenen Beispiele frei experimentieren kann. "Monte Carlo Methods in Finance" - ein unverzichtbares Nachschlagewerk für quantitative Analysten, die bei der Bewertung von Optionspreisen und Riskmanagement auf Modelle zurückgreifen müssen.

Exploring Monte Carlo Methods

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Author : William L. Dunn
language : en
Publisher: Elsevier
Release Date : 2022-06-07

Exploring Monte Carlo Methods written by William L. Dunn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-07 with Science categories.

Exploring Monte Carlo Methods, Second Edition provides a valuable introduction to the numerical methods that have come to be known as "Monte Carlo." This unique and trusted resource for course use, as well as researcher reference, offers accessible coverage, clear explanations and helpful examples throughout. Building from the basics, the text also includes applications in a variety of fields, such as physics, nuclear engineering, finance and investment, medical modeling and prediction, archaeology, geology and transportation planning. - Provides a comprehensive yet concise treatment of Monte Carlo methods - Uses the famous "Buffon's needle problem" as a unifying theme to illustrate the many aspects of Monte Carlo methods - Includes numerous exercises and useful appendices on: Certain mathematical functions, Bose Einstein functions, Fermi Dirac functions and Watson functions

Monte Carlo Methods In Financial Engineering

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Author : Paul Glasserman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Monte Carlo Methods In Financial Engineering written by Paul Glasserman 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 2013-03-09 with Mathematics categories.

Monte Carlo simulation has become an essential tool in the pricing of derivative securities and in risk management. These applications have, in turn, stimulated research into new Monte Carlo methods and renewed interest in some older techniques. This book develops the use of Monte Carlo methods in finance and it also uses simulation as a vehicle for presenting models and ideas from financial engineering. It divides roughly into three parts. The first part develops the fundamentals of Monte Carlo methods, the foundations of derivatives pricing, and the implementation of several of the most important models used in financial engineering. The next part describes techniques for improving simulation accuracy and efficiency. The final third of the book addresses special topics: estimating price sensitivities, valuing American options, and measuring market risk and credit risk in financial portfolios. The most important prerequisite is familiarity with the mathematical tools used to specify and analyze continuous-time models in finance, in particular the key ideas of stochastic calculus. Prior exposure to the basic principles of option pricing is useful but not essential. The book is aimed at graduate students in financial engineering, researchers in Monte Carlo simulation, and practitioners implementing models in industry. Mathematical Reviews, 2004: "... this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context."

Monte Carlo Simulation

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Author : Christopher Z. Mooney
language : en
Publisher: SAGE
Release Date : 1997-04-07

Monte Carlo Simulation written by Christopher Z. Mooney and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-07 with Mathematics categories.

Aimed at researchers across the social sciences, this book explains the logic behind the Monte Carlo simulation method and demonstrates its uses for social and behavioural research.

Monte Carlo Methods

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Author : J. Hammersley
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07

Monte Carlo Methods written by J. Hammersley 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 2013-03-07 with Social Science categories.

This monograph surveys the present state of Monte Carlo methods. we have dallied with certain topics that have interested us Although personally, we hope that our coverage of the subject is reasonably complete; at least we believe that this book and the references in it come near to exhausting the present range of the subject. On the other hand, there are many loose ends; for example we mention various ideas for variance reduction that have never been seriously appli(:d in practice. This is inevitable, and typical of a subject that has remained in its infancy for twenty years or more. We are convinced Qf:ver theless that Monte Carlo methods will one day reach an impressive maturity. The main theoretical content of this book is in Chapter 5; some readers may like to begin with this chapter, referring back to Chapters 2 and 3 when necessary. Chapters 7 to 12 deal with applications of the Monte Carlo method in various fields, and can be read in any order. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient. We assume that the reader has what might roughly be described as a 'graduate' knowledge of mathematics. The actual mathematical techniques are, with few exceptions, quite elementary, but we have freely used vectors, matrices, and similar mathematical language for the sake of conciseness.