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Product details
File Size: 7948 KB
Print Length: 648 pages
Publisher: Springer; Corrected edition (December 1, 2010)
Publication Date: October 15, 2004
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B000QCQV14
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The mathematics of extreme events, or the remote parts of the probability distributions, is a discipline on its own, more important than any other with respect to risk and decisions since some domains are dominated by the extremes: for the class of subexponential (and of course for the subclass of power laws) the tails ARE the story.Now this book is the bible for the field. It has been diligently updated. It is complete, in the sense that there is nothing of relevance that is not mentioned, treated, or referred to in the text. My business is hidden risk which starts where this book stops, and I need the most complete text for that.In spite of the momentous importance of the field, there is a very small number of mathematicians who deal with tail events; of these there is a smaller group who go both inside and outside the "Cramer conditions" (intuitively, thin-tailed or exponential decline).It is also a book that grows on you. I would have given it a 5 stars when I started using it; today I give it 6 stars, and certainly 7 next year.I am buying a second copy for the office. If I had to go on a desert island with 2 probability books, I would take Feller's two volumes (written >40 years ago) and this one.One housecleaning detail: buy the hardcover, not the paperback as the ink quality is weaker for the latter.
Nassim Taleb's review expresses my thoughts better than I could have ever hoped.To add a few thoughts, this reference was the backbone of my dissertation which relied heavily on the application of EVT to mathematical programming. For any question I have, I check this book first. Whenever the main text could not help me, the references section has not failed me yet and they alone deserve 5 stars. Complete this book and you are in a good position to read many research papers in EVT.I would not consider this a suitable text for undergraduates. Instead, read Modelling of Extreme Values by Stuart Coles. Measure theory is not required for the overwhelming majority of the text but one should still be very comfortable with the central subjects of probability theory, statistics, and stochastic processes before starting this one. The book has a good balance between rigor and intuition.This is the kind of reference where every single time I re-read a section, I happen to learn something new. Buy it!
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.
This is an excellent book either as a straight read or as a source. It is the most comprehensive and readable book I know in this field. This is achieved by skipping fundamental proofs - for those, see Sidney Resanick Heavy Tailed Phenomena http://www.amazon.com/Heavy-Tail-Phenomena-Probabilistic-Statistical-Engineering/dp/0387242724. That said, there are many longish but routine calculations which the narrative or'leaps. Its fun to work them out, but a clause or two like 'do this and this to see that...' would have helped.
Excellent book!
I learn all that I had to learn for my exam in this book. There are all the basics and even more complicated notions you need to understand extreme value theory.
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.
This book was new and in excennet condition.
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