Modelling Extremal Events: for Insurance and Finance (Stochastic Modelling and Applied Probability) (Hardcover)

by Paul Embrechts (Author), Claudia Klüppelberg (Author), Thomas Mikosch (Author) "For most of the problems treated in insurance mathematics, risk theory still provides the quintessential mathematical basis..." (more)
Key Phrases: Special Topics, Fluctuations of Maxima, Fluctuations of Upper Order Statistics (more...)

Editorial Reviews

Review
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."  

Product Description
Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increasingly important role. This book sets out to bridge the gap between the existing theory and practical applications both from a probabilistic as well as from a statistical point of view. Whatever new theory is presented is always motivated by relevant real-life examples. The numerous illustrations and examples, and the extensive bibliography make this book an ideal reference text for students, teachers and users in the industry of extremal event methodology.

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Product Details

• Hardcover: 655 pages
• Publisher: Springer; Corrected edition (June 2008)
• Language: English
• ISBN-10: 3540609318
• ISBN-13: 978-3540609315
• Product Dimensions: 9.4 x 6.2 x 1.6 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #218,730 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

48 of 50 people found the following review helpful:

4.0 out of 5 stars Highly recommended, August 14, 2000

By	Giuseppe A. Paleologo "gappy" (Riverdale, NY United States) - See all my reviews (REAL NAME)

This book covers the theory and applications of extremal value theory (an area of applied probability). The mathematics is kept at an acceptable level, i.e. advanced undergraduates in math/physics/engineering, but the breadth and the sophistication of the statements are such that the results are never trivial. Chapters 2-3-4 introduce the reader to the property of sums, maxima and order statistics of random variables. Many results are only stated but not proved. Yet, this does not detract to the readability of the book. Chpater 5 treats point processes and requires a deeper mathematical background. Among the chapters, this was the most disappointing to me. The monographs of Resnick and of Kallenberg, as well as many good introductions to point processes in queueing theory, are in my opinion both a more intuitive and rigorous introduction to random measures. This is not a major flaw of the book, given its view toward applications; and besides this, the bibliographical notes will point the reader to the relevant literature. Chapter 6, on statistical analysis of extremal events, is enjoyable and extremely useful for practitioners in finance and insurance. Chapter 7 touches upon time series and its relation to heavy tails. Finally, chapter 8 is a put-pourri of topics: ARCH processes, stable processes, self-similarity. Overall, I found this book useful as a reference, but sometimes lacking in focus: some topics seem juxtaposed with no clear logical continuity. Another potential shortcoming of the book is that it is neither completely rigorous nor completely readable (i.e., an undergraduate-level book). At the same time, these can be considered as qualities: with regards to the former, there is plenty of material to consult and draw inspiration from; and at the same time each reader will find the "right" level of mathematics in the book. In my opinion the final balance is largely positive, and I would recommend this book without hesitation.

25 of 25 people found the following review helpful:

5.0 out of 5 stars most detailed coverage on extremes and their application to finance, January 23, 2008

By	Michael R. Chernick "statman31147" (Holland PA) - See all my reviews (REAL NAME)

book presents extreme value theory and its applications with the finance industry as its primary target. There have been many excellent texts written on extreme value theory but none this extensive. As the authors admit even as extensive as it is the theory of multivariate extremes is neglected. They chose to only cover in detail the theory that is mature enough for application.
What you will find here that is not in many texts on this subject is a treatment of risk theory and fluctuations of sums and various time series models including cases with heavy-tailed marginal distributions.

Chapter 8 on special topics is particularly interesting with a lot of coverage for the extremal index, large claim index, ARCH processes, large deviations, reinsurance, stable processes and self-similarity. The book contains over 600 references to the literature and is a welcome resource for practitioners in finance and insurance as well as extreme value theorists.

12 of 12 people found the following review helpful:

5.0 out of 5 stars largest book written on extremes, January 29, 2002

By	Michael R. Chernick "statman13" (Malvern, PA) - See all my reviews (REAL NAME)

This book presents extreme value theory and its applications with the finance industry as its primary target. There have been many excellent texts written on extreme value theory but none this extensive. As the authors admit even as extensive as it is the theory of multivariate extremes is neglected. They chose to only cover in detail the theory that is mature enough for application.

What you will find here that is not in many texts on this subject is a treatment of risk theory and fluctuations of sums and various time series models including cases with heavy-tailed marginal distributions.

Chapter 8 on special topics is particularly interesting with a lot of coverage for the extremal index, large claim index, ARCH processes, large deviations, reinsurance, stable processes and self-similarity. The book contains over 600 references to the literature and is a welcome resource for practitioners in finance and insurance as well as extreme value theorists.