Author: Jan GóreckiPublisher: Springer Nature
ISBN: 3031563379
Category :
Languages : en
Pages : 128
Book Description
Hierarchical Archimedean Copulas
Author: Jan GóreckiPublisher: Springer Nature
ISBN: 3031563379
Category :
Languages : en
Pages : 128
Book Description
Properties of Hierarchical Archimedean Copulas
Author: Ostap OkhrinHierarchical Archimedean Copulas
Author: Ostap OkhrinArchimedean Copulas Derived from Morgenstern Utility Functions
Author: Jaap SpreeuwPublisher:
ISBN:
Category :
Languages : en
Pages : 31
Book Description
The (additive) generator of an Archimedean copula - as well as the inverse of the generator - is a strictly decreasing and convex function, while Morgenstern utility functions (applying to risk averse decision makers) are nondecreasing and concave. This provides a basis for deriving either a generator of Archimedean copulas, or its inverse, from a Morgenstern utility function. If we derive the generator itself in this way, dependence properties of an Archimedean copula that are often taken to be desirable, match with generally sought after properties of the corresponding utility function. If, on the other hand, we instead derive the inverse of the generator from the utility function, there is a link between the magnitude of measures of risk attitude (like the very common Arrow-Pratt coefficient of absolute risk aversion) and the strength of dependence featured by the corresponding Archimedean copula. For both methods some new copula families are derived, and their properties are discussed.
Copula Theory and Its Applications
Author: Piotr JaworskiPublisher: Springer Science & Business Media
ISBN: 3642124658
Category : Mathematics
Languages : en
Pages : 338
Book Description
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.
Time-varying Hierarchical Archimedean Copulas Using Adaptively Simulated Critical Values
Author: Ramona Theresa SteckSimulating Copulas
Author: Jan-Frederik MaiPublisher: World Scientific
ISBN: 1848168748
Category : Mathematics
Languages : en
Pages : 310
Book Description
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)
Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications (Second Edition)
Author: Jan-frederik MaiPublisher: #N/A
ISBN: 9813149264
Category : Mathematics
Languages : en
Pages : 357
Book Description
'The book remains a valuable tool both for statisticians who are already familiar with the theory of copulas and just need to develop sampling algorithms, and for practitioners who want to learn copulas and implement the simulation techniques needed to exploit the potential of copulas in applications.'Mathematical ReviewsThe 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.
Counting Statistics for Dependent Random Events
Author: Enrico BernardiPublisher: Springer Nature
ISBN: 303064250X
Category : Business & Economics
Languages : en
Pages : 206
Book Description
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.
Dependence Modeling with Copulas
Author: Harry JoePublisher: CRC Press
ISBN: 1466583223
Category : Mathematics
Languages : en
Pages : 483
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 factor models that extend from the Gaussian assumption to copulas. It also discusses other multivariate constructions and parametric copula families that have different tail properties and presents extensive material on dependence and tail properties to assist in copula model selection. The author shows how numerical methods and algorithms for inference and simulation are important in high-dimensional copula applications. He presents the algorithms as pseudocode, illustrating their implementation for high-dimensional copula models. He also incorporates results to determine dependence and tail properties of multivariate distributions for future constructions of copula models.