Introduction To Quasi Monte Carlo Integration And Applications
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Introduction To Quasi Monte Carlo Integration And Applications
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Author : Gunther Leobacher
language : en
Publisher: Springer
Release Date : 2014-09-12
Introduction To Quasi Monte Carlo Integration And Applications written by Gunther Leobacher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-12 with Mathematics categories.
This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed explanations comprises, for example, lattice rules, digital nets and sequences and discrepancy theory. It also presents methods currently used in research and discusses practical applications with an emphasis on finance-related problems. Each chapter closes with suggestions for further reading and with exercises which help students to arrive at a deeper understanding of the material presented. The book is based on a one-semester, two-hour undergraduate course and is well-suited for readers with a basic grasp of algebra, calculus, linear algebra and basic probability theory. It provides an accessible introduction for undergraduate students in mathematics or computer science.
Digital Nets And Sequences
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Author : Josef Dick
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-09
Digital Nets And Sequences written by Josef Dick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-09 with Computers categories.
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.
Monte Carlo And Quasi Monte Carlo Methods
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Author : Art B. Owen
language : en
Publisher: Springer
Release Date : 2018-07-03
Monte Carlo And Quasi Monte Carlo Methods written by Art B. Owen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Computers categories.
This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. 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, computer graphics and the solution of PDEs.
Quasi Monte Carlo Methods In Finance With Application To Optimal Asset Allocation
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Author : Mario Rometsch
language : en
Publisher: diplom.de
Release Date : 2014-04-11
Quasi Monte Carlo Methods In Finance With Application To Optimal Asset Allocation written by Mario Rometsch and has been published by diplom.de this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-11 with Mathematics categories.
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 [...]
Monte Carlo And Quasi Monte Carlo Methods 2000
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Author : Kai-Tai Fang
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Monte Carlo And Quasi Monte Carlo Methods 2000 written by Kai-Tai Fang 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 2011-06-28 with Mathematics categories.
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.
Monte Carlo And Quasi Monte Carlo Methods 2012
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Author : Josef Dick
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-05
Monte Carlo And Quasi Monte Carlo Methods 2012 written by Josef Dick 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 2013-12-05 with Mathematics categories.
This book represents the refereed proceedings of the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of New South Wales (Australia) in February 2012. 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, statistics and computer graphics.
Monte Carlo And Quasi Monte Carlo Methods
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Author : Aicke Hinrichs
language : en
Publisher: Springer Nature
Release Date : 2024-07-12
Monte Carlo And Quasi Monte Carlo Methods written by Aicke Hinrichs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-12 with Mathematics categories.
This book presents the refereed proceedings of the 15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held in Linz, Austria, and organized by the Johannes Kepler University Linz and the Austrian Academy of Sciences, in July 2022. 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 highly active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, in particular arising in finance, statistics and computer graphics.
Lattice Rules
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Author : Josef Dick
language : en
Publisher: Springer Nature
Release Date : 2022-07-23
Lattice Rules written by Josef Dick and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-23 with Mathematics categories.
Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.
Mathematical Analysis And Its Applications
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Author : P. N. Agrawal
language : en
Publisher: Springer
Release Date : 2015-08-22
Mathematical Analysis And Its Applications written by P. N. Agrawal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-22 with Mathematics categories.
This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical analysis and at promoting the exchange of ideas in various applications of mathematics in engineering, physics and biology. This conference encourages international collaboration and provides young researchers an opportunity to learn about the current state of the research in their respective fields.
Monte Carlo And Quasi Monte Carlo Methods In Scientific Computing
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Author : Harald Niederreiter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Monte Carlo And Quasi Monte Carlo Methods In Scientific Computing written by Harald Niederreiter 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 2012-12-06 with Mathematics categories.
Scientists and engineers are increasingly making use of simulation methods to solve problems which are insoluble by analytical techniques. Monte Carlo methods which make use of probabilistic simulations are frequently used in areas such as numerical integration, complex scheduling, queueing networks, and large-dimensional simulations. This collection of papers arises from a conference held at the University of Nevada, Las Vegas, in 1994. The conference brought together researchers across a range of disciplines whose interests include the theory and application of these methods. This volume provides a timely survey of this field and the new directions in which the field is moving.