On Copula Density Estimation And Measures Of Multivariate Association
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On Copula Density Estimation And Measures Of Multivariate Association
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Author : Thomas Blumentritt
language : en
Publisher: BoD – Books on Demand
Release Date : 2012
On Copula Density Estimation And Measures Of Multivariate Association written by Thomas Blumentritt and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Business & Economics categories.
Measuring the degree of association between random variables is a task inherent in many practical applications such as risk management and financial modeling. Well-known measures like Spearman's rho and Kendall's tau can be expressed in terms of the underlying copula only, hence, being independent of the underlying univariate marginal distributions. Opposed to these classical measures of association, mutual information, which is derived from information theory, constitutes a fundamentally different approach of measuring association. Although this measure is likewise independent of the univariate margins, it is not a functional of the copula but of the corresponding copula density. Besides the theoretical properties of mutual information as a measure of multivariate association, possibilities to estimate the copula density based on observations of continuous distributions are investigated. To cope with the effect of boundary bias, new estimators are introduced and existing functionals are generalized to the multivariate case. The performance of these estimators is evaluated in comparison to common kernel density estimation schemes. To facilitate variance estimation by means of resampling methods like bootstrapping, an algorithm is introduced, which significantly reduces computation time in comparison with pre-implemented algorithms. In practical applications, complete continuous data is oftentimes not available to the analyst. Instead, categorial data derived from the underlying continuous distribution may be given. Hence, estimation of the copula and its density based on contingency tables is investigated. The newly developed estimators are employed to derive estimates of Spearman's rho and Kendall's tau and their performance is compared.
High Dimensionality In Statistics And Portfolio Optimization
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Author : Konstantin Glombek
language : en
Publisher: BoD – Books on Demand
Release Date : 2012
High Dimensionality In Statistics And Portfolio Optimization written by Konstantin Glombek and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Safety And Reliability Of Complex Engineered Systems
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Author : Luca Podofillini
language : en
Publisher: CRC Press
Release Date : 2015-09-03
Safety And Reliability Of Complex Engineered Systems written by Luca Podofillini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-03 with Technology & Engineering categories.
Safety and Reliability of Complex Engineered Systems contains the Proceedings of the 25th European Safety and Reliability Conference, ESREL 2015, held 7-10 September 2015 in Zurich, Switzerland. It includes about 570 papers accepted for presentation at the conference. These contributions focus on theories and methods in the area of risk, safety and
Analyzing And Modeling Multivariate Association
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Author : Julius Schnieders
language : en
Publisher:
Release Date : 2013
Analyzing And Modeling Multivariate Association written by Julius Schnieders and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Multivariate Density Estimation
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Author : David W. Scott
language : en
Publisher:
Release Date : 2014
Multivariate Density Estimation written by David W. Scott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with MATHEMATICS categories.
Convolution Copula Econometrics
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Author : Umberto Cherubini
language : en
Publisher: Springer
Release Date : 2016-12-01
Convolution Copula Econometrics written by Umberto Cherubini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-01 with Business & Economics categories.
This book presents a novel approach to time series econometrics, which studies the behavior of nonlinear stochastic processes. This approach allows for an arbitrary dependence structure in the increments and provides a generalization with respect to the standard linear independent increments assumption of classical time series models. The book offers a solution to the problem of a general semiparametric approach, which is given by a concept called C-convolution (convolution of dependent variables), and the corresponding theory of convolution-based copulas. Intended for econometrics and statistics scholars with a special interest in time series analysis and copula functions (or other nonparametric approaches), the book is also useful for doctoral students with a basic knowledge of copula functions wanting to learn about the latest research developments in the field.
Copula Theory And Its Applications
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Author : Piotr Jaworski
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-16
Copula Theory And Its Applications written by Piotr Jaworski 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 2010-07-16 with Mathematics categories.
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.
Copula Methods In Finance
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Author : Umberto Cherubini
language : en
Publisher: John Wiley & Sons
Release Date : 2004-10-22
Copula Methods In Finance written by Umberto Cherubini and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-22 with Business & Economics categories.
Copula Methods in Finance is the first book to address the mathematics of copula functions illustrated with finance applications. It explains copulas by means of applications to major topics in derivative pricing and credit risk analysis. Examples include pricing of the main exotic derivatives (barrier, basket, rainbow options) as well as risk management issues. Particular focus is given to the pricing of asset-backed securities and basket credit derivative products and the evaluation of counterparty risk in derivative transactions.
Contributions To Static And Time Varying Copula Based Modeling Of Multivariate Association
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Author : Martin Ruppert
language : en
Publisher: BoD – Books on Demand
Release Date : 2012
Contributions To Static And Time Varying Copula Based Modeling Of Multivariate Association written by Martin Ruppert and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Business & Economics categories.
Putting a particular emphasis on nonparametric methods that rely on modern empirical process techniques, the author contributes to the theory of static and time-varying stochastic models for multivariate association based on the concept of copulas. These functions enable a profound understanding of multivariate association, which is pivotal for judging whether a large set of risky assets entails diversification effects or aggravates risk from an entrepreneurial point of view. Since serial dependence is a stylized fact of financial time series, an asymptotic theory for estimating the structure of association in this context is developed under weak assumptions. A new measure of multivariate association, based on a notion of distance to stochastic independence, is introduced. Asymptotic results as well as hypothesis tests are established which are directly applicable to important types of multivariate financial time series. To ensure that risk management properly captures the current structure of association, it is crucial to assess the constancy of the structure. Therefore, nonparametric tests for a constant copula with either a specified or unspecified change point (candidate) are derived. The thesis concludes with a study of characterizations of association between non-continuous random variables.
Risk Measurement
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Author : Dominique Guégan
language : en
Publisher: Springer
Release Date : 2019-03-22
Risk Measurement written by Dominique Guégan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-22 with Business & Economics categories.
This book combines theory and practice to analyze risk measurement from different points of view. The limitations of a model depend on the framework on which it has been built as well as specific assumptions, and risk managers need to be aware of these when assessing risks. The authors investigate the impact of these limitations, propose an alternative way of thinking that challenges traditional assumptions, and also provide novel solutions. Starting with the traditional Value at Risk (VaR) model and its limitations, the book discusses concepts like the expected shortfall, the spectral measure, the use of the spectrum, and the distortion risk measures from both a univariate and a multivariate perspective.