Actuarial Modelling Of Extremal Events Using Transformed Generalized Extreme Value Distributions And Generalized Pareto Distributions
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Actuarial Modelling Of Extremal Events Using Transformed Generalized Extreme Value Distributions And Generalized Pareto Distributions
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Author : Zhongxian Han
language : en
Publisher:
Release Date : 2003
Actuarial Modelling Of Extremal Events Using Transformed Generalized Extreme Value Distributions And Generalized Pareto Distributions written by Zhongxian Han and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Extreme value theory categories.
Abstract: In 1928, Extreme Value Theory (EVT) originated in work of Fisher and Tippett describing the behavior of maximum of independent and identically distributed random variables. Various applications have been implemented successfully in many fields such as: actuarial science, hydrology, climatology, engineering, and economics and finance. This paper begins with introducing examples that extreme value theory comes to encounter. Then classical results from EVT are reviewed and the current research approaches are introduced. In particular, statistical methods are emphasized in detail for the modeling of extremal events. A case study of hurricane damages over the last century is presented using the "excess over threshold" (EOT) method. In most actual cases, the range of the data collected is finite with an upper bound while the fitted Generalized Extreme Value (GEV) and Generalized Pareto (GPD) distributions have infinite tails. Traditionally this is treated as trivial based on the assumption that the upper bound is so large that no significant result is affected when it is replaced by infinity. However, in certain circumstances, the models can be improved by implementing more specific techniques. Different transforms are introduced to rescale the GEV and GPD distributions so that they have finite supports. All classical methods can be applied directly to transformed models if the upper bound is known. In case the upper bound is unknown, we set up models with one additional parameter based on transformed distributions. Properties of the transform functions are studied and applied to find the cumulative density functions (cdfs) and probability density functions (pdfs) of the transformed distributions. We characterize the transformed distribution from the plots of their cdfs and mean residual life. Then we apply our findings to determine which transformed distribution should be used in the models. At the end some results of parameter estimation are obtained through the maximum likelihood method.
Modelling Extremal Events
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Author : Paul Embrechts
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Modelling Extremal Events written by Paul Embrechts 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 2013-03-14 with Business & Economics categories.
"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
Extreme Value Modeling And Risk Analysis
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Author : Dipak K. Dey
language : en
Publisher: CRC Press
Release Date : 2016-01-06
Extreme Value Modeling And Risk Analysis written by Dipak K. Dey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-06 with Mathematics categories.
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
Computational Actuarial Science With R
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Author : Arthur Charpentier
language : en
Publisher: CRC Press
Release Date : 2014-08-26
Computational Actuarial Science With R written by Arthur Charpentier and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-26 with Business & Economics categories.
A Hands-On Approach to Understanding and Using Actuarial Models Computational Actuarial Science with R provides an introduction to the computational aspects of actuarial science. Using simple R code, the book helps you understand the algorithms involved in actuarial computations. It also covers more advanced topics, such as parallel computing and C/C++ embedded codes. After an introduction to the R language, the book is divided into four parts. The first one addresses methodology and statistical modeling issues. The second part discusses the computational facets of life insurance, including life contingencies calculations and prospective life tables. Focusing on finance from an actuarial perspective, the next part presents techniques for modeling stock prices, nonlinear time series, yield curves, interest rates, and portfolio optimization. The last part explains how to use R to deal with computational issues of nonlife insurance. Taking a do-it-yourself approach to understanding algorithms, this book demystifies the computational aspects of actuarial science. It shows that even complex computations can usually be done without too much trouble. Datasets used in the text are available in an R package (CASdatasets).
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 2004
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Dissertations, Academic categories.
Mathematical And Statistical Methods For Actuarial Sciences And Finance
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Author : Marco Corazza
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-07
Mathematical And Statistical Methods For Actuarial Sciences And Finance written by Marco Corazza 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 2011-06-07 with Mathematics categories.
This book features selected papers from the international conference MAF 2008 that cover a wide variety of subjects in actuarial, insurance and financial fields, all treated in light of the successful cooperation between mathematics and statistics.
Extreme Value Distributions
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Author : Samuel Kotz
language : en
Publisher: World Scientific
Release Date : 2000-01-01
Extreme Value Distributions written by Samuel Kotz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
(Imperial College Press) A monograph describing the central ideas and results of probabilistic extreme-value theory and related models stemming from the work of E. J. Gumbel in the early 1940s. An up-to-date extensive bibliography supplements the invariate and multivariate distributions and their applications. DLC: Extreme value theory.
Statistics Of Extremes
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Author : Jan Beirlant
language : en
Publisher: John Wiley & Sons
Release Date : 2006-03-17
Statistics Of Extremes written by Jan Beirlant 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 2006-03-17 with Mathematics categories.
Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.
Advances In Heavy Tailed Risk Modeling
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Author : Gareth W. Peters
language : en
Publisher: John Wiley & Sons
Release Date : 2015-05-26
Advances In Heavy Tailed Risk Modeling written by Gareth W. Peters 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 2015-05-26 with Mathematics categories.
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.
Extreme Value Theory And Applications
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Author : J. Galambos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Extreme Value Theory And Applications written by J. Galambos 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 2013-12-01 with Mathematics categories.
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.