Sampling Nested Archimedean Copulas

Author : Jan Marius Hofert
Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
Page : 200 pages
File Size : 48,5 Mb
Release : 2010
Category : Electronic
ISBN : 3838116569

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Sampling Nested Archimedean Copulas by Jan Marius Hofert Pdf

Copulas are distribution functions with standard uniform univariate margins. A famous class of copulas consists of Archimedean copulas, which are constructed by a one-dimensional function called the generator of the Archimedean copula. In large-dimensional applications the symmetry of Archimedean copulas is often considered to be a drawback. By nesting Archimedean copulas at different levels, one obtains the more general and flexible class of nested Archimedean copulas. The present work explores these copulas. In particular, efficient sampling algorithms, especially suited for large dimensions, are presented. From the practitioner's point of view, fast sampling algorithms are required for large-scale simulation studies. Efficiently sampling nested Archimedean copulas requires sampling from certain distributions which are related to the generators of the Archimedean copulas involved via Laplace-Stieltjes transforms. The work at hand presents efficient strategies for sampling these distributions. As an application, a pricing model for collateralized debt obligations is developed which precisely captures the given hierarchical structure of such a credit-risky portfolio.

Author : Jan Górecki
Publisher : Springer Nature
Page : 128 pages
File Size : 48,9 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 9783031563379

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Hierarchical Archimedean Copulas by Jan Górecki Pdf

Author : Piotr Jaworski,Fabrizio Durante,Wolfgang Karl Härdle,Tomasz Rychlik
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 55,6 Mb
Release : 2010-07-16
Category : Mathematics
ISBN : 9783642124655

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Copula Theory and Its Applications by Piotr Jaworski,Fabrizio Durante,Wolfgang Karl Härdle,Tomasz Rychlik Pdf

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.

Author : Marius Hofert,Ivan Kojadinovic,Martin Mächler,Jun Yan
Publisher : Springer
Page : 267 pages
File Size : 45,6 Mb
Release : 2019-01-09
Category : Business & Economics
ISBN : 9783319896359

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Elements of Copula Modeling with R by Marius Hofert,Ivan Kojadinovic,Martin Mächler,Jun Yan Pdf

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 : Jan-Frederik Mai,Matthias Scherer
Publisher : World Scientific
Page : 312 pages
File Size : 42,6 Mb
Release : 2012-06-26
Category : Mathematics
ISBN : 9781908977588

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Simulating Copulas by Jan-Frederik Mai,Matthias Scherer Pdf

This book provides the reader with a background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology. Errata(s) Errata (128 KB) Sample Chapter(s) Chapter 1: Introduction (1,016 KB) Chapter 4: Elliptical Copulas (857 KB) Contents:IntroductionArchimedean CopulasMarshall–Olkin CopulasElliptical CopulasPair Copula ConstructionsSampling Univariate Random VariablesThe Monte Carlo Method Readership: Advanced undergraduate and graduate students in probability calculus and stochastics, practitioners who implement models in the financial industry and scientists. Keywords:Copula;Simulation;Monte Carlo;Random Vector;Dependence ModelKey Features:Explicit focus on stochastic representations of copulas in contrast to an analytical perspectiveEasy-to-implement simulation schemes given as pseudo codeExplicit focus on high-dimensional modelsFocus on applicability of models, e.g. to portfolio credit risk or insuranceReviews:“The book is essentially self-contained, as the reader interested in copulas from the simulation point of view will find all necessary material in it, including an introduction to copulas if he has never been exposed to them. Both the theoretical and practical frameworks emerge quite clearly from the book. In any case, the rich bibliography contains all the references required for further in-depth analyses of specific issues. I think that the authors did a very good job, filling a gap in the statistical literature and providing a contribution that is going to be particularly helpful to statisticians without a specific background in copulas. ”Mathematical Reviews

Author : Scherer Matthias,Mai Jan-frederik
Publisher : #N/A
Page : 356 pages
File Size : 45,8 Mb
Release : 2017-06-07
Category : Mathematics
ISBN : 9789813149267

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Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications (Second Edition) by Scherer Matthias,Mai Jan-frederik Pdf

The book provides the background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for graduate and advanced undergraduate students with a firm background in stochastics. Besides the theoretical foundation, ready-to-implement algorithms and many examples make the book a valuable tool for anyone who is applying the methodology.

Author : Umberto Cherubini,Sabrina Mulinacci,Fabio Gobbi,Silvia Romagnoli
Publisher : John Wiley & Sons
Page : 287 pages
File Size : 46,8 Mb
Release : 2011-10-20
Category : Business & Economics
ISBN : 9781119954521

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Dynamic Copula Methods in Finance by Umberto Cherubini,Sabrina Mulinacci,Fabio Gobbi,Silvia Romagnoli Pdf

The latest tools and techniques for pricing and risk management This book introduces readers to the use of copula functions to represent the dynamics of financial assets and risk factors, integrated temporal and cross-section applications. The first part of the book will briefly introduce the standard the theory of copula functions, before examining the link between copulas and Markov processes. It will then introduce new techniques to design Markov processes that are suited to represent the dynamics of market risk factors and their co-movement, providing techniques to both estimate and simulate such dynamics. The second part of the book will show readers how to apply these methods to the evaluation of pricing of multivariate derivative contracts in the equity and credit markets. It will then move on to explore the applications of joint temporal and cross-section aggregation to the problem of risk integration.

Author : Harry Joe
Publisher : CRC Press
Page : 479 pages
File Size : 41,7 Mb
Release : 2014-06-26
Category : Mathematics
ISBN : 9781466583238

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Dependence Modeling with Copulas by Harry Joe Pdf

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 : Enrico Bernardi,Silvia Romagnoli
Publisher : Springer Nature
Page : 206 pages
File Size : 44,5 Mb
Release : 2021-03-22
Category : Business & Economics
ISBN : 9783030642501

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Counting Statistics for Dependent Random Events by Enrico Bernardi,Silvia Romagnoli Pdf

This book on counting statistics presents a novel copula-based approach to counting dependent random events. It combines clustering, combinatorics-based algorithms and dependence structure in order to tackle and simplify complex problems, without disregarding the hierarchy of or interconnections between the relevant variables. These problems typically arise in real-world applications and computations involving big data in finance, insurance and banking, where experts are confronted with counting variables in monitoring random events. In this new approach, combinatorial distributions of random events are the core element. In order to deal with the high-dimensional features of the problem, the combinatorial techniques are used together with a clustering approach, where groups of variables sharing common characteristics and similarities are identified and the dependence structure within groups is taken into account. The original problems can then be modeled using new classes of copulas, referred to here as clusterized copulas, which are essentially based on preliminary groupings of variables depending on suitable characteristics and hierarchical aspects. The book includes examples and real-world data applications, with a special focus on financial applications, where the new algorithms’ performance is compared to alternative approaches and further analyzed. Given its scope, the book will be of interest to master students, PhD students and researchers whose work involves or can benefit from the innovative methodologies put forward here. It will also stimulate the empirical use of new approaches among professionals and practitioners in finance, insurance and banking.

Author : Marcelo G. Cruz,Gareth W. Peters,Pavel V. Shevchenko
Publisher : John Wiley & Sons
Page : 928 pages
File Size : 40,8 Mb
Release : 2015-01-29
Category : Mathematics
ISBN : 9781118573006

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Fundamental Aspects of Operational Risk and Insurance Analytics by Marcelo G. Cruz,Gareth W. Peters,Pavel V. Shevchenko Pdf

A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk, the handbook also features: Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework Guidelines for how operational risk can be inserted into a firm’s strategic decisions A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.

Author : Harry Joe,Dorota Kurowicka
Publisher : World Scientific
Page : 370 pages
File Size : 51,7 Mb
Release : 2011
Category : Business & Economics
ISBN : 9789814299886

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Dependence Modeling by Harry Joe,Dorota Kurowicka Pdf

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 : Annalisa Appice,Michelangelo Ceci,Corrado Loglisci,Giuseppe Manco,Elio Masciari,Zbigniew W. Ras
Publisher : Springer
Page : 265 pages
File Size : 44,7 Mb
Release : 2014-07-05
Category : Computers
ISBN : 9783319084077

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New Frontiers in Mining Complex Patterns by Annalisa Appice,Michelangelo Ceci,Corrado Loglisci,Giuseppe Manco,Elio Masciari,Zbigniew W. Ras Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the Second International Workshop on New Frontiers in Mining Complex Patterns, NFMCP 2013, held in conjunction with ECML/PKDD 2013 in Prague, Czech Republic, in September 2013. The 16 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on data streams and time series analysis, classification, clustering and pattern discovery, graphs, networks and relational data, machine learning and music data.

Author : Piotr Kulczycki,Janusz Kacprzyk,László T. Kóczy,Radko Mesiar,Rafal Wisniewski
Publisher : Springer
Page : 384 pages
File Size : 54,7 Mb
Release : 2019-04-17
Category : Technology & Engineering
ISBN : 9783030180584

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Information Technology, Systems Research, and Computational Physics by Piotr Kulczycki,Janusz Kacprzyk,László T. Kóczy,Radko Mesiar,Rafal Wisniewski Pdf

This book highlights a broad range of modern information technology tools, techniques, investigations and open challenges, mainly with applications in systems research and computational physics. Divided into three major sections, it begins by presenting specialized calculation methods in the framework of data analysis and intelligent computing. In turn, the second section focuses on application aspects, mainly for systems research, while the final section investigates how various tasks in the basic disciplines—mathematics and physics—can be tackled with the aid of contemporary IT methods. The book gathers selected presentations from the 3rd Conference on Information Technology, Systems Research and Computational Physics (ITSRCP'18), which took place on 2–5 July 2018 in Krakow, Poland. The intended readership includes interdisciplinary scientists and practitioners pursuing research at the interfaces of information technology, systems research, and computational physics.

Author : Rui Wang,Zengqiang Chen,Weicun Zhang,Quanmin Zhu
Publisher : Springer Nature
Page : 1340 pages
File Size : 54,7 Mb
Release : 2019-12-03
Category : Technology & Engineering
ISBN : 9789811504747

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Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019) by Rui Wang,Zengqiang Chen,Weicun Zhang,Quanmin Zhu Pdf

This book includes original, peer-reviewed research papers from the 11th International Conference on Modelling, Identification and Control (ICMIC2019), held in Tianjin, China on July 13-15, 2019. The topics covered include but are not limited to: System Identification, Linear/Nonlinear Control Systems, Data-driven Modelling and Control, Process Modelling and Process Control, Fault Diagnosis and Reliable Control, Intelligent Systems, and Machine Learning and Artificial Intelligence.The papers showcased here share the latest findings on methodologies, algorithms and applications in modelling, identification, and control, integrated with Artificial Intelligence (AI), making the book a valuable asset for researchers, engineers, and university students alike.

Author : Lan Zhang,V. P. Singh
Publisher : Cambridge University Press
Page : 621 pages
File Size : 49,9 Mb
Release : 2019-01-10
Category : Mathematics
ISBN : 9781108474252

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Copulas and Their Applications in Water Resources Engineering by Lan Zhang,V. P. Singh Pdf

Illustration of copula theory with detailed real-world case study examples in the fields of hydrology and water resources engineering.