Download or read book Dependent Risk Models with Archimedean Copulas written by Hélène Cossette and published by . This book was released on 2017 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we investigate dependent risk models in which the dependence structure is defined by an Archimedean copula. Using such a structure with specific marginals, we derive explicit expressions for the pdf of the aggregated risk and other related quantities. The common mixture representation of Archimedean copulas is at the basis of a computational strategy proposed to find exact or approximated values of the distribution of the sum of risks in a general setup. Such results are then used to investigate risk models in regard to aggregation, capital allocation and ruin problems. An extension to nested Archimedean copulas is also discussed.
Download or read book Archimedean Copula Based Models in Financial Risk Management written by Qing Xu and published by LAP Lambert Academic Publishing. This book was released on 2009-06-14 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copula is used to model multivariate data, as it accounts for the dependence structure and provides a flexible representation of the multivariate distribution. Recently a large number of Archimedean copulas have been proposed to deal with various dependence aspects in financial risk management, which invokes several new questions in some important yet under-researched areas.This dissertation comprises three essays and probes into three untouched questions all involving the Archimedean-copula-based models. It provides important empirical evidences that the Archimedean copula-based PVaR model generally has better forecasting performance than the Gaussian copula-based PVaR model. Therefore, financial risk managers should consider the use of the Archimedean copula-based PVaR model when attempting to forecast extreme downside dependent risk.
Download or read book Dependence Modeling with Copulas written by Harry Joe and published by CRC Press. This book was released on 2014-06-26 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Actuarial Theory for Dependent Risks written by Michel Denuit and published by John Wiley & Sons. This book was released on 2006-05-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing complexity of insurance and reinsurance products has seen a growing interest amongst actuaries in the modelling of dependent risks. For efficient risk management, actuaries need to be able to answer fundamental questions such as: Is the correlation structure dangerous? And, if yes, to what extent? Therefore tools to quantify, compare, and model the strength of dependence between different risks are vital. Combining coverage of stochastic order and risk measure theories with the basics of risk management and stochastic dependence, this book provides an essential guide to managing modern financial risk. * Describes how to model risks in incomplete markets, emphasising insurance risks. * Explains how to measure and compare the danger of risks, model their interactions, and measure the strength of their association. * Examines the type of dependence induced by GLM-based credibility models, the bounds on functions of dependent risks, and probabilistic distances between actuarial models. * Detailed presentation of risk measures, stochastic orderings, copula models, dependence concepts and dependence orderings. * Includes numerous exercises allowing a cementing of the concepts by all levels of readers. * Solutions to tasks as well as further examples and exercises can be found on a supporting website. An invaluable reference for both academics and practitioners alike, Actuarial Theory for Dependent Risks will appeal to all those eager to master the up-to-date modelling tools for dependent risks. The inclusion of exercises and practical examples makes the book suitable for advanced courses on risk management in incomplete markets. Traders looking for practical advice on insurance markets will also find much of interest.
Download or read book Collective Risk Models with Dependence written by Hélène Cossette and published by . This book was released on 2018 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such distributions in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.
Download or read book Copulas and Dependence Models with Applications written by Manuel Úbeda Flores and published by Springer. This book was released on 2017-10-13 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Hierarchical Archimedean Copula for Portfolio Credit Risk Modelling written by Natalia Tente and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: I introduce a novel, hierarchical model of tail dependent asset returns which can be particularly useful for measuring portfolio credit risk within the structural framework. To allow for a stronger dependence within sub-portfolios than between them, I utilise the concept of nested Archimedean copulas, but modify the nesting procedure to ensure the compatibility of copula generators by construction. This makes sampling straightforward. Moreover, I provide details on a particular specification based on a gamma mixture of powers. This model allows for lower tail dependence, resulting in a more conservative credit risk assessment than a comparable Gaussian model. I illustrate the extent of model risk when calculating VaR or Expected Shortfall for a credit portfolio.
Download or read book Hierarchical Archimedean Copulas written by Jan Górecki and published by Springer Nature. This book was released on with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Copula Modeling with R written by Marius Hofert and published by Springer. This book was released on 2019-01-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Hierarchical Archimedean Copula for Portfolio Credit Risk Modelling written by Natalia Puzanova and published by . This book was released on 2016 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: I introduce a novel, hierarchical model of tail dependent asset returns which can be particularly useful for measuring portfolio credit risk within the structural framework. To allow for a stronger dependence within sub-portfolios than between them, I utilise the concept of nested Archimedean copulas, but modify the nesting procedure to ensure the compatibility of copula generators by construction. This makes sampling straightforward. Moreover, I provide details on a particular specification based on a gamma mixture of powers. This model allows for lower tail dependence, resulting in a more conservative credit risk assessment than a comparable Gaussian model. I illustrate the extent of model risk when calculating VaR or Expected Shortfall for a credit portfolio.
Download or read book Dependence Modeling written by Harry Joe and published by World Scientific. This book was released on 2011 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Financial Engineering with Copulas Explained written by J. Mai and published by Springer. This book was released on 2014-10-02 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a succinct guide to the application and modelling of dependence models or copulas in the financial markets. First applied to credit risk modelling, copulas are now widely used across a range of derivatives transactions, asset pricing techniques and risk models and are a core part of the financial engineer's toolkit.
Download or read book Risk Management written by M. A. H. Dempster and published by Cambridge University Press. This book was released on 2002-01-10 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of derivative products in risk management has spread from commodities, stocks and fixed income items, to such virtual commodities as energy, weather and bandwidth. All this can give rise to so-called volatility and there has been a consequent development in formal risk management techniques to cover all types of risk: market, credit, liquidity, etc. One of these techniques, Value at Risk, was developed specifically to help manage market risk over short periods. Its success led, somewhat controversially, to its take up and extension to credit risk over longer time-scales. This extension, ultimately not successful, led to the collapse of a number of institutions. The present book, which was originally published in 2002, by some of the leading figures in risk management, examines the complex issues that concern the stability of the global financial system by presenting a mix of theory and practice.
Download or read book Copula Theory and Its Applications written by Piotr Jaworski and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modeling Dependence Induced by a Common Random Effect and Risk Measures with Insurance Applications written by Junjie Liu and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random effects models are of particular importance in modeling heterogeneity. A commonly used random effects model for multivariate survival analysis is the frailty model. In this thesis, a special frailty model with an Archimedean dependence structure is used to model dependent risks. This modeling approach allows the construction of multivariate distributions through a copula with univariate marginal distributions as parameters. Copulas are constructed by modeling distribution functions and survival functions, respectively. Measures of the dependence are applied for the copula model selections. Tail-based risk measures for the functions of two dependent variables are investigated for particular interest. The statistical application of the copula modeling approach to an insurance data set is discussed where losses and loss adjustment expenses data are used. Insurance applications based on the fitted model are illustrated.
Download or read book Analysis of Survival Data with Dependent Censoring written by Takeshi Emura and published by Springer. This book was released on 2018-04-05 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to copula-based statistical methods for analyzing survival data involving dependent censoring. Primarily focusing on likelihood-based methods performed under copula models, it is the first book solely devoted to the problem of dependent censoring. The book demonstrates the advantages of the copula-based methods in the context of medical research, especially with regard to cancer patients’ survival data. Needless to say, the statistical methods presented here can also be applied to many other branches of science, especially in reliability, where survival analysis plays an important role. The book can be used as a textbook for graduate coursework or a short course aimed at (bio-) statisticians. To deepen readers’ understanding of copula-based approaches, the book provides an accessible introduction to basic survival analysis and explains the mathematical foundations of copula-based survival models.
Download or read book Heavy Tails And Copulas Topics In Dependence Modelling In Economics And Finance written by Rustam Ibragimov and published by World Scientific. This book was released on 2017-02-24 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Overall, the book is highly technical, including full mathematical proofs of the results stated. Potential readers are post-graduate students or researchers in Quantitative Risk Management willing to have a manual with the state-of-the-art on portfolio diversification and risk aggregation with heavy tails, including the fundamental theorems as well as collateral (but most useful) results on majorization and copula theory.'Quantitative Finance This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence.
