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Extreme Value Modeling And Risk Analysis
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Book Synopsis Extreme Value Modeling and Risk Analysis by : Dipak K. Dey
Download or read book Extreme Value Modeling and Risk Analysis written by Dipak K. Dey and published by CRC Press. This book was released on 2016-01-06 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subje
Book Synopsis Recent Studies on Risk Analysis and Statistical Modeling by : Teresa A. Oliveira
Download or read book Recent Studies on Risk Analysis and Statistical Modeling written by Teresa A. Oliveira and published by Springer. This book was released on 2018-08-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the latest developments in the field of risk analysis (RA). Statistical methodologies have long-since been employed as crucial decision support tools in RA. Thus, in the context of this new century, characterized by a variety of daily risks - from security to health risks - the importance of exploring theoretical and applied issues connecting RA and statistical modeling (SM) is self-evident. In addition to discussing the latest methodological advances in these areas, the book explores applications in a broad range of settings, such as medicine, biology, insurance, pharmacology and agriculture, while also fostering applications in newly emerging areas. This book is intended for graduate students as well as quantitative researchers in the area of RA.
Book Synopsis Information Theoretic Approach to Statistics of Extremes by : Ganbaatar Jambal
Download or read book Information Theoretic Approach to Statistics of Extremes written by Ganbaatar Jambal and published by . This book was released on 2018 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extreme Value Theory is a special field of statistics which is often used in modeling and analyzing behavior of extreme and rare events. This theory has well-established theoretical foundations, and it finds fruitful applications in various fields of science. These fields include, but are not limited to, finance and insurance, information technology and telecommunications, environmental science, wind engineering and aerodynamics, food science, biomedical and clinical data processing, DNA analysis, and management. Despite the well-established theoretical foundations, researchers still tend to encounter a number of issues when trying to solve practical problems using the Extreme Value Theory. These problems are often associated with limitations of common estimators. For instance, the maximum likelihood method fails to meet the regularity conditions for a range of values of underlying parameters of Extreme Value Models. Method of Moments and its variations are often advocated as `viable' alternatives to the maximum likelihood method, but, in some cases, they tend to yield nonsensical parameter estimates which tend contradict the data used in estimations. In addition, the common estimation methods suffer from other serious shortcomings as well: including sensitivity of parameter estimates, convergence problems, tendency to misspecify submodels of Extreme Value Distributions, and complexity caused by strict functional and distributional assumptions. This dissertation uses info-metrics framework to develop new estimation methods for Extreme Value Models. Main motivations are as follows: (a) the info-metrics framework relaxes rigid assumptions inherent in the common estimation methods, e.g. the rigid assumption of strict fulfillment of zero-moment conditions; (b) the info-metrics framework provides convenient tools to deal with the under-determined problems; (c) the framework also allows researchers to address the fundamental uncertainty related to model discrimination; (d) the framework can be beneficial in cases where the data is noisy; (e) the info-metrics framework also allows to incorporate covariates and regressors into Extreme Value Models without adding complexity. Simulation results and empirical examples of this dissertation demonstrate that the flexibility of the info-metrics framework can address several shortcomings of common estimators of Extreme Value Models: (a) reduces sensitivity of parameter estimates; (b) mitigates the problem of misspecication of submodels of Extreme Value Distributions; (c) demonstrates superior performance compared to common estimations methods, especially in cases where the sample size is small, and the data is noisy; (d) in many cases, the info-metrics framework is able to achieve the desired finite-sample properties and empirical conclusions without making strict assumption regarding the data-generating process.
Book Synopsis Extreme Value Theory with Applications to Natural Hazards by : Nicolas Bousquet
Download or read book Extreme Value Theory with Applications to Natural Hazards written by Nicolas Bousquet and published by Springer Nature. This book was released on 2021-10-09 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated book describes statistical extreme value theory for the quantification of natural hazards, such as strong winds, floods and rainfall, and discusses an interdisciplinary approach to allow the theoretical methods to be applied. The approach consists of a number of steps: data selection and correction, non-stationary theory (to account for trends due to climate change), and selecting appropriate estimation techniques based on both decision-theoretic features (e.g., Bayesian theory), empirical robustness and a valid treatment of uncertainties. It also examines and critically reviews alternative approaches based on stochastic and dynamic numerical models, as well as recently emerging data analysis issues and presents large-scale, multidisciplinary, state-of-the-art case studies. Intended for all those with a basic knowledge of statistical methods interested in the quantification of natural hazards, the book is also a valuable resource for engineers conducting risk analyses in collaboration with scientists from other fields (such as hydrologists, meteorologists, climatologists).
Book Synopsis An Introduction to Statistical Modeling of Extreme Values by : Stuart Coles
Download or read book An Introduction to Statistical Modeling of Extreme Values written by Stuart Coles and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Directly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.
Book Synopsis Operational Risk by : Anna S. Chernobai
Download or read book Operational Risk written by Anna S. Chernobai and published by John Wiley & Sons. This book was released on 2007-06-15 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operational Risk While operational risk has long been regarded as a mere part of "other" risks—outside the realm of credit and market risk—it has quickly made its way to the forefront of finance. In fact, with implementation of the Basel II Capital Accord already underway, many financial professionals—as well as those preparing to enter this field—must now become familiar with a variety of issues related to operational risk modeling and management. Written by the experienced team of Anna Chernobai, Svetlozar Rachev, and Frank Fabozzi, Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis will introduce you to the key concepts associated with this discipline. Filled with in-depth insights, expert advice, and innovative research, this comprehensive guide not only presents you with an abundant amount of information regarding operational risk, but it also walks you through a wide array of examples that will solidify your understanding of the issues discussed. Topics covered include: The main challenges that exist in modeling operational risk The variety of approaches used to model operational losses Value-at-Risk and its role in quantifying and managing operational risk The three pillars of the Basel II Capital Accord And much more
Book Synopsis Statistical Methods on Risk Management of Extreme Events by : Zijing Zhang
Download or read book Statistical Methods on Risk Management of Extreme Events written by Zijing Zhang and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the dissertation is the investigation of financial risk analysis methodologies, using the schemes for extreme value modeling as well as techniques from copula modeling. Extreme value theory is concerned with probabilistic and statistical questions re- lated to unusual behavior or rare events. The subject has a rich mathematical theory and also a long tradition of applications in a variety of areas. We are interested in its application in risk management, with a focus on estimating and forcasting the Value-at-Risk of financial time series data. Extremal data are inherently scarce, thus making inference challenging. In order to obtain good estimates for risk measures, we develop a two-stage approach: (1) fitting the GARCH-type models at the first stage to describe the volatility clustering and other stylized facts of financial time series; (2) using the extreme value theory based models to fit to the tails of the residuals. Additionally, the performance measures provide information in terms of the comparison of the two-stage semi-parametric approach with the parametric methodologies, through robust backtesting. Copula is a particular branch of probability theory, with which, given sufficient data, we can separate the marginal behavior of individual risks and their dependence structure from a multivariate random variable. Linear correlation is widely used to model dependence but has limitations as a measure of association and thus we opt to use copulas to analyze the dependence structure and build models for our different problems arising in risk management. For this part of the dissertation, we take a look at different copula families, highlight for some when they are most appropriate to use for a particular application, discuss some of their drawbacks as diverse scenarios occur in different risk management models, and explore the possibility of developing the copula modeling to reflect the complicated dependence structure of portfolios.
Book Synopsis Extreme and Systemic Risk Analysis by : Stefan Hochrainer-Stigler
Download or read book Extreme and Systemic Risk Analysis written by Stefan Hochrainer-Stigler and published by Springer Nature. This book was released on 2020-04-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about how extreme and systemic risk can be analyzed in an integrated way. Risk analysis is understood to include measurement, assessment as well as management aspects. Integration is understood as being able to perform risk analysis for extreme and systemic events simultaneously. The presented approach is based on Sklar's theorem, which states that a multivariate distribution can be separated into two parts – one describing the marginal distributions and the other describing the dependency between the distributions using a so-called copula. It is suggested to reinterpret Sklar's theorem from a system or network perspective, treating copulas as a network property and individual, including extreme, risk as elements within the network. In that way, extreme and systemic risk can be analyzed independently as well as jointly across several scales. The book is intended for a large audience, and all techniques presented are guided with examples and applications with a special focus on natural disaster events. Furthermore, an extensive literature and discussion of it are given in each chapter for the interested reader.
Book Synopsis Statistical Analysis of Extreme Values by : Rolf-Dieter Reiss
Download or read book Statistical Analysis of Extreme Values written by Rolf-Dieter Reiss and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical analysis of extreme data is vital to many disciplines including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to parametric modeling, exploratory analysis and statistical interference for extreme values. For this Third Edition, the entire text has been thoroughly updated and rearranged to meet contemporary requirements, with new sections and chapters address such topics as dependencies, the conditional analysis and the multivariate modeling of extreme data. New chapters include An Overview of Reduced-Bias Estimation; The Spectral Decomposition Methodology; About Tail Independence; and Extreme Value Statistics of Dependent Random Variables.
Book Synopsis Modelling Extremal Events by : Paul Embrechts
Download or read book Modelling Extremal Events written by Paul Embrechts and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A reader's first impression on leafing through this book is of the large number of graphs and diagrams, used to illustrate shapes of distributions...and to show real data examples in various ways. A closer reading reveals a nice mix of theory and applications, with the copious graphical illustrations alluded to. Such a mixture is of course dear to the heart of the applied probabilist/statistician, and should impress even the most ardent theorists." --MATHEMATICAL REVIEWS
Book Synopsis Extreme Value Analysis of Actuarial Risks by : Holger Drees
Download or read book Extreme Value Analysis of Actuarial Risks written by Holger Drees and published by . This book was released on 2011 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic analysis of extreme value estimators and to devise tools for the validation of the underlying model assumptions. While the focus of the paper is on univariate tail risk analysis, the basic ideas of the analysis of the extremal dependence between different risks are also outlined. Here we emphasize some of the limitations of classical multivariate extreme value theory and sketch how a different model proposed by Ledford and Tawn can help to avoid pitfalls. Finally, these theoretical results are used to analyze a data set of large claim sizes from health insurance.
Book Synopsis Extreme Value Theory and Applications by : J. Galambos
Download or read book Extreme Value Theory and Applications written by J. Galambos and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: It appears that we live in an age of disasters: the mighty Missis sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening. While all these may seem to be unexpected phenomena to the man on the street, they are actually happening according to well defined rules of science known as extreme value theory. We know that records must be broken in the future, so if a flood design is based on the worst case of the past then we are not really prepared against floods. Materials will fail due to fatigue, so if the body of an aircraft looks fine to the naked eye, it might still suddenly fail if the aircraft has been in operation over an extended period of time. Our theory has by now penetrated the so cial sciences, the medical profession, economics and even astronomy. We believe that our field has come of age. In or~er to fully utilize the great progress in the theory of extremes and its ever increasing acceptance in practice, an international conference was organized in which equal weight was given to theory and practice. This book is Volume I of the Proceedings of this conference. In selecting the papers for Volume lour guide was to have authoritative works with a large variety of coverage of both theory and practice.
Book Synopsis Extreme Value Methods with Applications to Finance by : Serguei Y. Novak
Download or read book Extreme Value Methods with Applications to Finance written by Serguei Y. Novak and published by CRC Press. This book was released on 2011-12-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers—in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible. Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers: Extremes in samples of random size Methods of estimating extreme quantiles and tail probabilities Self-normalized sums of random variables Measures of market risk Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text. A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.
Book Synopsis Extreme Events in Finance by : Francois Longin
Download or read book Extreme Events in Finance written by Francois Longin and published by John Wiley & Sons. This book was released on 2016-10-17 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the growing importance of extreme value risk theory, methods, and applications in the financial sector Presenting a uniquely accessible guide, Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications features a combination of the theory, methods, and applications of extreme value theory (EVT) in finance and a practical understanding of market behavior including both ordinary and extraordinary conditions. Beginning with a fascinating history of EVTs and financial modeling, the handbook introduces the historical implications that resulted in the applications and then clearly examines the fundamental results of EVT in finance. After dealing with these theoretical results, the handbook focuses on the EVT methods critical for data analysis. Finally, the handbook features the practical applications and techniques and how these can be implemented in financial markets. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications includes: Over 40 contributions from international experts in the areas of finance, statistics, economics, business, insurance, and risk management Topical discussions on univariate and multivariate case extremes as well as regulation in financial markets Extensive references in order to provide readers with resources for further study Discussions on using R packages to compute the value of risk and related quantities The book is a valuable reference for practitioners in financial markets such as financial institutions, investment funds, and corporate treasuries, financial engineers, quantitative analysts, regulators, risk managers, large-scale consultancy groups, and insurers. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications is also a useful textbook for postgraduate courses on the methodology of EVTs in finance.
Book Synopsis Extreme Values and Financial Risk by : Saralees Nadarajah
Download or read book Extreme Values and Financial Risk written by Saralees Nadarajah and published by MDPI. This book was released on 2019-01-15 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Extreme Values and Financial Risk" that was published in JRFM
Book Synopsis New Extreme Value Theory for Heterogeneous Data by : Wenzhi Cao
Download or read book New Extreme Value Theory for Heterogeneous Data written by Wenzhi Cao and published by . This book was released on 2020 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigorous risk analysis helps to make better decisions and prevent great failures. Extreme value theory has been a powerful tool in risk analysis and widely applied to risk analysis in finance, insurance, health, climate, and environmental studies. In classical extreme value theory, the sequence of data is assumed to have the same marginal distribution and the limiting distribution of the maxima is in one of the extreme value types if it exists. Although advanced statistical models have been proposed to fit complex data better, the advances of science and technology have generated more complex data, e.g., Big Data, in which existing probability theory and statistical models find their limitations. This work establishes probability foundations for studying extreme values of data generated from a mixture process with the mixture pattern depending on the sample length. In particular, we show that the limit distribution of the maxima of a sequence of random variables with the above mixture pattern is a product of three types of extreme value distributions termed as the sub-max-stable distributions. As a result, our theoretical results are more general than the classical extreme value theory and can be applicable to research problems related to Big Data. Examples are provided to give intuitions of the new distribution family. The classical results for the Poisson property of exceedances of high thresholds are extended under this mixture pattern. We also establish mixing conditions for a sequence of random variables to have the limit distributions. The results for the associated independent sequence and the maxima over arbitrary intervals are also developed. We use simulations to demonstrate the advantages of our established theory.
Book Synopsis Extreme Events in Finance by : Francois Longin
Download or read book Extreme Events in Finance written by Francois Longin and published by John Wiley & Sons. This book was released on 2016-09-30 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the growing importance of extreme value risk theory, methods, and applications in the financial sector Presenting a uniquely accessible guide, Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications features a combination of the theory, methods, and applications of extreme value theory (EVT) in finance and a practical understanding of market behavior including both ordinary and extraordinary conditions. Beginning with a fascinating history of EVTs and financial modeling, the handbook introduces the historical implications that resulted in the applications and then clearly examines the fundamental results of EVT in finance. After dealing with these theoretical results, the handbook focuses on the EVT methods critical for data analysis. Finally, the handbook features the practical applications and techniques and how these can be implemented in financial markets. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications includes: Over 40 contributions from international experts in the areas of finance, statistics, economics, business, insurance, and risk management Topical discussions on univariate and multivariate case extremes as well as regulation in financial markets Extensive references in order to provide readers with resources for further study Discussions on using R packages to compute the value of risk and related quantities The book is a valuable reference for practitioners in financial markets such as financial institutions, investment funds, and corporate treasuries, financial engineers, quantitative analysts, regulators, risk managers, large-scale consultancy groups, and insurers. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications is also a useful textbook for postgraduate courses on the methodology of EVTs in finance.
