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Author: Marius Hofert
Publisher: Springer
ISBN: 3319896350
Category : Business & Economics
Languages : en
Pages : 274
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Book Description
This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.
Author: Marius Hofert
Publisher: Springer
ISBN: 3319896350
Category : Business & Economics
Languages : en
Pages : 274
Get Book Here
Book Description
This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.
Author: Pravin K. Trivedi
Publisher: Now Publishers Inc
ISBN: 1601980205
Category : Business & Economics
Languages : en
Pages : 126
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Book Description
Copula Modeling explores the copula approach for econometrics modeling of joint parametric distributions. Copula Modeling demonstrates that practical implementation and estimation is relatively straightforward despite the complexity of its theoretical foundations. An attractive feature of parametrically specific copulas is that estimation and inference are based on standard maximum likelihood procedures. Thus, copulas can be estimated using desktop econometric software. This offers a substantial advantage of copulas over recently proposed simulation-based approaches to joint modeling. Copulas are useful in a variety of modeling situations including financial markets, actuarial science, and microeconometrics modeling. Copula Modeling provides practitioners and scholars with a useful guide to copula modeling with a focus on estimation and misspecification. The authors cover important theoretical foundations. Throughout, the authors use Monte Carlo experiments and simulations to demonstrate copula properties
Author: Harry Joe
Publisher: World Scientific
ISBN: 981429988X
Category : Business & Economics
Languages : en
Pages : 370
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Book Description
1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka
Author: Harry Joe
Publisher: CRC Press
ISBN: 1466583231
Category : Mathematics
Languages : en
Pages : 479
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Book Description
Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured facto
Author: Roger B. Nelsen
Publisher: Springer Science & Business Media
ISBN: 1475730764
Category : Mathematics
Languages : en
Pages : 227
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Book Description
Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.
Author: Fabrizio Durante
Publisher: CRC Press
ISBN: 1439884447
Category : Mathematics
Languages : en
Pages : 331
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Book Description
This book gives readers the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures. The authors prove the results as simply as possible and unify various methods scattered throughout the literature in common frameworks, including shuffles of copulas. They also explore connections with related functions, such as quasi-copulas, semi-copulas, and triangular norms, that have been used in different domains.
Author: Claudia Czado
Publisher:
ISBN: 9783030137861
Category : Copulas (Mathematical statistics)
Languages : en
Pages :
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Book Description
This textbook provides a step-by-step introduction to the class of vine copulas, their statistical inference and applications. It focuses on statistical estimation and selection methods for vine copulas in data applications. These flexible copula models can successfully accommodate any form of tail dependence and are vital to many applications in finance, insurance, hydrology, marketing, engineering, chemistry, aviation, climatology and health. The book explains the pair-copula construction principles underlying these statistical models and discusses how to perform model selection and inference. It also derives simulation algorithms and presents real-world examples to illustrate the methodological concepts. The book includes numerous exercises that facilitate and deepen readers understanding, and demonstrates how the R package VineCopula can be used to explore and build statistical dependence models from scratch. In closing, the book provides insights into recent developments and open research questions in vine copula based modeling. The book is intended for students as well as statisticians, data analysts and any other quantitatively oriented researchers who are new to the field of vine copulas. Accordingly, it provides the necessary background in multivariate statistics and copula theory for exploratory data tools, so that readers only need a basic grasp of statistics and probability.
Author: Damiano Brigo
Publisher: John Wiley & Sons
ISBN: 0470971436
Category : Business & Economics
Languages : en
Pages : 212
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Book Description
The recent financial crisis has highlighted the need for better valuation models and risk management procedures, better understanding of structured products, and has called into question the actions of many financial institutions. It has become commonplace to blame the inadequacy of credit risk models, claiming that the crisis was due to sophisticated and obscure products being traded, but practitioners have for a long time been aware of the dangers and limitations of credit models. It would seem that a lack of understanding of these models is the root cause of their failures but until now little analysis had been published on the subject and, when published, it had gained very limited attention. Credit Models and the Crisis is a succinct but technical analysis of the key aspects of the credit derivatives modeling problems, tracing the development (and flaws) of new quantitative methods for credit derivatives and CDOs up to and through the credit crisis. Responding to the immediate need for clarity in the market and academic research environments, this book follows the development of credit derivatives and CDOs at a technical level, analyzing the impact, strengths and weaknesses of methods ranging from the introduction of the Gaussian Copula model and the related implied correlations to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time. It also illustrates the implied copula, a method that can consistently account for CDOs with different attachment and detachment points but not for different maturities, and explains why the Gaussian Copula model is still used in its base correlation formulation. The book reports both alarming pre-crisis research and market examples, as well as commentary through history, using data up to the end of 2009, making it an important addition to modern derivatives literature. With banks and regulators struggling to fully analyze at a technical level, many of the flaws in modern financial models, it will be indispensable for quantitative practitioners and academics who want to develop stable and functional models in the future.
Author: Manuel Úbeda Flores
Publisher: Springer
ISBN: 3319642219
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This book presents contributions and review articles on the theory of copulas and their applications. The authoritative and refereed contributions review the latest findings in the area with emphasis on “classical” topics like distributions with fixed marginals, measures of association, construction of copulas with given additional information, etc. The book celebrates the 75th birthday of Professor Roger B. Nelsen and his outstanding contribution to the development of copula theory. Most of the book’s contributions were presented at the conference “Copulas and Their Applications” held in his honor in Almería, Spain, July 3-5, 2017. The chapter 'When Gumbel met Galambos' is published open access under a CC BY 4.0 license.
Author: Arkady Shemyakin
Publisher: John Wiley & Sons
ISBN: 1118959027
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC,Bayesian regression, and Bayesian analysis of statistical modelsof dependence, and features a focus on copulas for risk management Introduction to Bayesian Estimation and Copula Models of Dependence emphasizes the applications of Bayesian analysis to copula modeling and equips readers with the tools needed to implement the procedures of Bayesian estimation in copula models of dependence. This book is structured in two parts: the first four chapters serve as a general introduction to Bayesian statistics with a clear emphasis on parametric estimation and the following four chapters stress statistical models of dependence with a focus of copulas. A review of the main concepts is discussed along with the basics of Bayesian statistics including prior information and experimental data, prior and posterior distributions, with an emphasis on Bayesian parametric estimation. The basic mathematical background of both Markov chains and Monte Carlo integration and simulation is also provided. The authors discuss statistical models of dependence with a focus on copulas and present a brief survey of pre-copula dependence models. The main definitions and notations of copula models are summarized followed by discussions of real-world cases that address particular risk management problems. In addition, this book includes: • Practical examples of copulas in use including within the Basel Accord II documents that regulate the world banking system as well as examples of Bayesian methods within current FDA recommendations • Step-by-step procedures of multivariate data analysis and copula modeling, allowing readers to gain insight for their own applied research and studies • Separate reference lists within each chapter and end-of-the-chapter exercises within Chapters 2 through 8 • A companion website containing appendices: data files and demo files in Microsoft® Office Excel®, basic code in R, and selected exercise solutions Introduction to Bayesian Estimation and Copula Models of Dependence is a reference and resource for statisticians who need to learn formal Bayesian analysis as well as professionals within analytical and risk management departments of banks and insurance companies who are involved in quantitative analysis and forecasting. This book can also be used as a textbook for upper-undergraduate and graduate-level courses in Bayesian statistics and analysis. ARKADY SHEMYAKIN, PhD, is Professor in the Department of Mathematics and Director of the Statistics Program at the University of St. Thomas. A member of the American Statistical Association and the International Society for Bayesian Analysis, Dr. Shemyakin's research interests include informationtheory, Bayesian methods of parametric estimation, and copula models in actuarial mathematics, finance, and engineering. ALEXANDER KNIAZEV, PhD, is Associate Professor and Head of the Department of Mathematics at Astrakhan State University in Russia. Dr. Kniazev's research interests include representation theory of Lie algebras and finite groups, mathematical statistics, econometrics, and financial mathematics.
