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Modelling Extremal Events

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Table of Contents

Reader Guidelines.- Risk Theory.- Fluctuations of Sums.- Fluctuations of Maxima.- Fluctuations of Upper Order Statistics.- An Approach to Extremes via Point Processes.- Statistical Methods for Extremal Events.- Time Series Analysis for Heavy-Tailed Processes.- Special Topics.

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Corrected 2nd print


From the reviews: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION "...excellent, comprehensive treatise on the subject of extremal events modeling. The authors have responded well to the demands of extreme value practitioners for such a text. Although it was clearly and admittedly motivated by practical questions of workers in finance, insurance, and reinsurance, [the book] contains the mathematical rigor and generality that will interest the extreme value theoretician...An understanding of modes of convergence, specifically weak convergence, is essential to fully appreciate the text, but the authors' intuitive writing style makes most of the basic ideas accessible even to the uninitiated...The authors do an excellent job of organizing these topics and also provide a very useful 20-page `Reader Guidelines' section...[the book] makes an excellent contribution to unifying important concepts in extreme value theory and modeling of extremal events. Aside from its obvious use as a reference for practitioners and theoreticians alike, this text may be used to teach a graduate-level course in mathematical finance or a special topics course in stochastic processes with or without a financial emphasis...As the authors point out this may not be the kind of book that you want to tackle form cover to cover initially, but it is my bet you will eventually discover that you have done just that as you repeatedly reference this hefty volume throughout the years." MATHEMATICAL REVIEWS/MATHSCINET DATABASE "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, to plot sample paths of various processes 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 with the range of applications of the subject. While there are a number of books available which cover most of the topics herein, I know of none which presents such a range of theory and applications of extremal processes in one volume, at a level easily understood by users of the methodology. I highly recommend the book to all who work in the area, or in related areas. (...) The combination of skills and expertise of the three authors of this book is impressive. Their reading covers not only the traditional and classical works in the area but a great deal of the modern development, too. (They give 646 references to books and articles in the literature.) Their book concludes with copious appendices setting out the basic probability theory and some of the regular variation theory required for understanding the rest of the development. In summary, this is a worthwhile book in an extremely important area." SIAM REVIEWS "(...) This book impresses me as being exceptionally well written, scholarly beyond question, more than a little daunting, and likely to become a classic in its field." KWANTITIEWE METHODEN "The book is the first in the area that strikes a proper balance between mathematical rigor and scope (...) and the statistically-oriented applications for the practitioner." EXTREMES "(...) the indispensable starting point for anyone interested in contemporary applications and extensions of classical EVT." MATHEMATICS TODAY "This is an encyclopedic handbook of theory and statistical praxis, of great value to actuaries and statisticians in the fields concerned, which gives an up to date picture of this fast developing field, and at the same time a useful and well motivated text book for those who need a guide for entering the area without getting lost either in pure theory or messy practice." ASTIN BULLETIN "Given the nature of the subject (...) the book is easy to read.(...) The narrative style is marvellous, invariably connecting theoretical concepts to the real world objects they are supposed to describe, (...)." RISKBOOK.COM "There are a number of texts available on Extreme Value Theory (EVT). This is the essential one to read. It is authoritative and extremely well written...A nice feature of Embrechts et al is an opening 20-page `reader guideline' that gives an overview of the material before the start of the main text."

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