Customer Reviews

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

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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.

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.

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.

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.

This book is one of the key references in extreme value theory and in actuarial risk theory. It is a complete and well written reference for theoretical and applied scientists. It is certainly one of my favorite references.