Explorations in Monte Carlo Methods

Author: Ronald W. Shonkwiler
Publisher: Springer Science & Business Media
ISBN: 9780387878379
Release Date: 2009-08-11
Genre: Mathematics

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. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. 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.

Finance with Monte Carlo

Author: Ronald W. Shonkwiler
Publisher: Springer Science & Business Media
ISBN: 9781461485117
Release Date: 2013-09-17
Genre: Mathematics

This text introduces upper division undergraduate/beginning graduate students in mathematics, finance, or economics, to the core topics of a beginning course in finance/financial engineering. Particular emphasis is placed on exploiting the power of the Monte Carlo method to illustrate and explore financial principles. Monte Carlo is the uniquely appropriate tool for modeling the random factors that drive financial markets and simulating their implications. The Monte Carlo method is introduced early and it is used in conjunction with the geometric Brownian motion model (GBM) to illustrate and analyze the topics covered in the remainder of the text. Placing focus on Monte Carlo methods allows for students to travel a short road from theory to practical applications. Coverage includes investment science, mean-variance portfolio theory, option pricing principles, exotic options, option trading strategies, jump diffusion and exponential Lévy alternative models, and the Kelly criterion for maximizing investment growth. Novel features: inclusion of both portfolio theory and contingent claim analysis in a single text pricing methodology for exotic options expectation analysis of option trading strategies pricing models that transcend the Black–Scholes framework optimizing investment allocations concepts thoroughly explored through numerous simulation exercises numerous worked examples and illustrations The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language. The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language. Also by the author: (with F. Mendivil) Explorations in Monte Carlo, ©2009, ISBN: 978-0-387-87836-2; (with J. Herod) Mathematical Biology: An Introduction with Maple and Matlab, Second edition, ©2009, ISBN: 978-0-387-70983-3.

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.

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.

Accelerating Monte Carlo methods for Bayesian inference in dynamical models

Author: Johan Dahlin
Publisher: Linköping University Electronic Press
ISBN: 9789176857977
Release Date: 2016-03-22
Genre:

Making decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ. The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). That is, strategies for reducing the computational effort while keeping or improving the accuracy. A major part of the thesis is devoted to proposing such strategies for the MCMC method known as the particle Metropolis-Hastings (PMH) algorithm. We investigate two strategies: (i) introducing estimates of the gradient and Hessian of the target to better tailor the algorithm to the problem and (ii) introducing a positive correlation between the point-wise estimates of the target. Furthermore, we propose an algorithm based on the combination of SMC and Gaussian process optimisation, which can provide reasonable estimates of the posterior but with a significant decrease in computational effort compared with PMH. Moreover, we explore the use of sparseness priors for approximate inference in over-parametrised mixed effects models and autoregressive processes. This can potentially be a practical strategy for inference in the big data era. Finally, we propose a general method for increasing the accuracy of the parameter estimates in non-linear state space models by applying a designed input signal.

Wahrscheinlichkeitstheorie und Stochastische Prozesse

Author: Michael Mürmann
Publisher: Springer-Verlag
ISBN: 9783642381607
Release Date: 2013-11-22
Genre: Mathematics

Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

Monte Carlo Strategies in Scientific Computing

Author: Jun S. Liu
Publisher: Springer Science & Business Media
ISBN: 0387952306
Release Date: 2001
Genre: Business & Economics

A large number of scientists and engineers employ Monte Carlo simulation and related global optimization techniques (such as simulated annealing) as an essential tool in their work. For such scientists, there is a need to keep up to date with several recent advances in Monte Carlo methodologies such as cluster methods, data-augmentation, simulated tempering and other auxiliary variable methods. There is also a trend in moving towards a population-based approach. All these advances in one way or another were motivated by the need to sample from very complex distribution for which traditional methods would tend to be trapped in local energy minima. This work aims to provide a self-contained treatment of the Monte Carlo method to this audience.

Introducing Monte Carlo Methods with R

Author: Christian Robert
Publisher: Springer Science & Business Media
ISBN: 9781441915757
Release Date: 2010
Genre: Computers

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.

Monte Carlo and Quasi Monte Carlo Methods 2010

Author: Leszek Plaskota
Publisher: Springer Science & Business Media
ISBN: 9783642274404
Release Date: 2012-08-23
Genre: Mathematics

This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. 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. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.

Monte Carlo and Quasi Monte Carlo Methods

Author: Ronald Cools
Publisher: Springer
ISBN: 9783319335070
Release Date: 2016-06-13
Genre: Mathematics

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.

Multicomponent Aerosol Dynamics

Author: Dharanipathy Rangaraj
Publisher:
ISBN: OCLC:58838351
Release Date: 2004
Genre: Aerosols, Radioactive

Computation of aerosol evolution is a problem of interest in many disciplines. We have explored applications of Direct Simulation Monte Carlo [DSMC] to some test problems. Multicomponent composite aerosols with constant coagulation have been studied with DSMC. It has been found that the result agrees quite well with exact and sectional results. Use of Multicomponent Brownian coagulation model also has been studied with DSMC and it had been found that for constant component density DSMC agrees well with the sectional results. The DSMC has however permitted computation of aerosol evolution when component densities are different, a condition which cannot be unambiguously studied by use of the sectional method. The computational requirement for DSMC technique has been studied and parallel computing option has been explored. A parallel computing environment was constructed. The computational power and time efficiency that can be obtained from parallel computing has been studied with the same test problems.

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.

Parallel Monte Carlo Tree Search for HPC Systems and its Application to Computer Go

Author: Lars Schäfers
Publisher: Logos Verlag Berlin GmbH
ISBN: 9783832537487
Release Date: 2014-07-29
Genre: Computers

Monte-Carlo Tree Search (MCTS) is a class of simulation-based search algorithms. It brought about great success in the past few years regarding the evaluation of deterministic two-player games such as the Asian board game Go. In this thesis, we present a parallelization of the most popular MCTS variant for large HPC compute clusters that efficiently shares a single game tree representation in a distributed memory environment and scales up to 128 compute nodes and 2048 cores. It is hereby one of the most powerful MCTS parallelizations to date. In order to measure the impact of our parallelization on the search quality and remain comparable to the most advanced MCTS implementations to date, we implemented it in a state-of-the-art Go engine Gomorra, making it competitive with the strongest Go programs in the world. We further present an empirical comparison of different Bayesian ranking systems when being used for predicting expert moves for the game of Go and introduce a novel technique for automated detection and analysis of evaluation uncertainties that show up during MCTS searches.

Image Analysis Random Fields and Markov Chain Monte Carlo Methods

Author: Gerhard Winkler
Publisher: Springer Science & Business Media
ISBN: 3540442138
Release Date: 2003
Genre: Computers

CD-ROM (version a 1.01) includes: software "AntsInFields", graphical user interfaces, an an educational, self explaining, and self contained library of living documents.--Intro. p. 5.

Vorticity Statistical Mechanics and Monte Carlo Simulation

Author: Chjan Lim
Publisher: Springer Science & Business Media
ISBN: 9780387494319
Release Date: 2007-07-28
Genre: Mathematics

This book is drawn from across many active fields of mathematics and physics. It has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access interesting, original, and publishable research in statistical modeling of large-scale flows and several related fields. The authors explicitly reach around the major branches of mathematics and physics, showing how the use of a few straightforward approaches can create a cornucopia of intriguing questions and the tools to answer them.