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Author : Jayakrishnan Nair,Adam Wierman,Bert Zwart
Publisher : Cambridge University Press
Page : 265 pages
File Size : 42,6 Mb
Release : 2022-06-09
Category : Business & Economics
ISBN : 9781316511732
An accessible yet rigorous package of probabilistic and statistical tools for anyone who must understand or model extreme events.
Author : Remigijus Leipus,Jonas Šiaulys,Dimitrios Konstantinides
Publisher : Springer Nature
Page : 99 pages
File Size : 47,9 Mb
Release : 2023-10-16
Category : Mathematics
ISBN : 9783031345531
This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.
Author : John P. Nolan
Publisher : Springer Nature
Page : 342 pages
File Size : 41,7 Mb
Release : 2020-09-13
Category : Mathematics
ISBN : 9783030529154
This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.
Author : Gareth W. Peters,Pavel V. Shevchenko
Publisher : John Wiley & Sons
Page : 667 pages
File Size : 46,5 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9781118909539
ADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes. A companion with Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the handbook provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distribution approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modeling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The handbook is also useful for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
Author : Ibragimov Rustam,Prokhorov Artem
Publisher : World Scientific
Page : 304 pages
File Size : 53,9 Mb
Release : 2017-02-24
Category : Business & Economics
ISBN : 9789814689816
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.
Author : Natalia Markovich
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 50,7 Mb
Release : 2008-03-11
Category : Mathematics
ISBN : 0470723599
Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution. The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function. Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.
Author : Rustam Ibragimov,Artem Prokhorov
Publisher : Unknown
Page : 303 pages
File Size : 51,7 Mb
Release : 2017
Category : BUSINESS & ECONOMICS
ISBN : 9814689807
"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."--Publisher's website.
Author : S.T Rachev
Publisher : Elsevier
Page : 707 pages
File Size : 52,5 Mb
Release : 2003-03-05
Category : Business & Economics
ISBN : 9780080557731
The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series should present an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. The goal is to have a broad group of outstanding volumes in various areas of finance. The Handbook of Heavy Tailed Distributions in Finance is the first handbook to be published in this series. This volume presents current research focusing on heavy tailed distributions in finance. The contributions cover methodological issues, i.e., probabilistic, statistical and econometric modelling under non- Gaussian assumptions, as well as the applications of the stable and other non -Gaussian models in finance and risk management.
Author : Mark M. Meerschaert,Hans-Peter Scheffler
Publisher : John Wiley & Sons
Page : 515 pages
File Size : 50,7 Mb
Release : 2001-07-11
Category : Mathematics
ISBN : 9780471356295
A comprehensive introduction to the central limit theory-from foundations to current research This volume provides an introduction to the central limit theory of random vectors, which lies at the heart of probability and statistics. The authors develop the central limit theory in detail, starting with the basic constructions of modern probability theory, then developing the fundamental tools of infinitely divisible distributions and regular variation. They provide a number of extensions and applications to probability and statistics, and take the reader through the fundamentals to the current level of research. In synthesizing results from nearly 200 research papers and presenting them in a self-contained form, authors Meerschaert and Scheffler have produced an accessible reference that treats the central limit theory honestly and focuses on multivariate models. For researchers, it provides an efficient and logical path through a large collection of results with many possible applications to real-world phenomena. Limit Distributions for Sums of Independent Random Vectors includes a coherent introduction to limit distributions and these other features: * A self-contained introduction to the multivariate problem * Multivariate regular variation for linear operators, real-valued functions, and Borel Measures * Multivariate limit theorems: limit distributions, central limit theorems, and related limit theorems * Real-world applications Limit Distributions for Sums of Independent Random Vectors is a comprehensive reference that provides an up-to-date survey of the state of the art in this important research area.
Author : Mark M. Meerschaert,Hans-Peter Scheffler
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 54,7 Mb
Release : 2001-07-11
Category : Mathematics
ISBN : 0471356298
Die Quintessenz aus über 100 Originalarbeiten! Ausgehend von den Grundpfeilern der modernen Wahrscheinlichkeitstheorie entwickeln die Autoren dieses in sich geschlossenen, gut verständlich formulierten Bandes die Theorie der unendlich teilbaren Verteilungen und der regulären Variation. Im Anschluss erarbeiten sie die allgemeine Grenzwerttheorie für unabhängige Zufallsvektoren. Dabei achten sie sorgfältig darauf, alle Aspekte in den Kontext der Wahrscheinlichkeitslehre und Statistik zu stellen und bieten dafür eine Fülle von Zusatzinformationen an.
Author : Andrew C. Harvey
Publisher : Cambridge University Press
Page : 128 pages
File Size : 49,9 Mb
Release : 2013-04-22
Category : Business & Economics
ISBN : 9781107328785
The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.
Author : Avrim Blum,John Hopcroft,Ravindran Kannan
Publisher : Cambridge University Press
Page : 433 pages
File Size : 51,6 Mb
Release : 2020-01-23
Category : Computers
ISBN : 9781108485067
Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.
Author : Marcelo G. Cruz,Gareth W. Peters,Pavel V. Shevchenko
Publisher : John Wiley & Sons
Page : 928 pages
File Size : 55,5 Mb
Release : 2015-01-20
Category : Mathematics
ISBN : 9781118573020
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 : Peter Wilson
Publisher : Unknown
Page : 352 pages
File Size : 47,7 Mb
Release : 2009
Category : Business & Economics
ISBN : UOM:39015080722898
In the last three decades, China and Thailand have undergone rapid economic growth and social change. Using theory, institutional analysis, and case studies, Economic Policies and Social Welfare in the 21st Century explores the challenges faced by the two countries during this period, such as how to compete in a world of volatile exchange rates and capital flows, how to open up the banking and communications sectors, environmental issues, and how to deal with social problems, such as health care and child rearing. Their responses through social and economic policies are then examined, including the transfer of technology, and fiscal and public policies.Social science students, teachers, and researchers, in both the government and private sectors, will find this book particularly relevant for understanding the process of growth and development in two of the most successful developing countries in the Asian region. Also available in the Gale Virtual Reference Library (eBook).eBook pricing varies according to the size of your institution. Please contact us for details.eBook ISBN-13: 9789814253697Available Now
Author : Rand R. Wilcox
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 48,5 Mb
Release : 2010-03-18
Category : Social Science
ISBN : 9781441955241
Conventional statistical methods have a very serious flaw. They routinely miss differences among groups or associations among variables that are detected by more modern techniques, even under very small departures from normality. Hundreds of journal articles have described the reasons standard techniques can be unsatisfactory, but simple, intuitive explanations are generally unavailable. Situations arise where even highly nonsignificant results become significant when analyzed with more modern methods. Without assuming the reader has any prior training in statistics, Part I of this book describes basic statistical principles from a point of view that makes their shortcomings intuitive and easy to understand. The emphasis is on verbal and graphical descriptions of concepts. Part II describes modern methods that address the problems covered in Part I. Using data from actual studies, many examples are included to illustrate the practical problems with conventional procedures and how more modern methods can make a substantial difference in the conclusions reached in many areas of statistical research. The second edition of this book includes a number of advances and insights that have occurred since the first edition appeared. Included are new results relevant to medians, regression, measures of association, strategies for comparing dependent groups, methods for dealing with heteroscedasticity, and measures of effect size.
