another fine book by Resnick

books:


	• Heavy-Tail Phenomena: Probabilistic and Statistical Modeling (Springer Series in Operations Research and ... Sidney I. Resnick Springer, 2006 - 406 pages average customer review:based on 2 reviews view larger image
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another fine book by Resnick

Sid Resnick taught me stochastic processes when I was a graduate student at Stanford. He is an exceptional lecturer who really stimulates the students. I don't think I ever had a boring lecture from him even though probability theory and stochastic processes can at times be very dry subjects.

Over the many years since then Sid has moved on and spent many fruitful years at Colorado State and now Cornell. In addition to his many excellent papers and his fine collaborative work with Richard Davis, he has written a large number of very interesting and thought provoking texts on extreme value theory, stochastic processes and probability theory. I have a deep appreciation for his contributions to the theory of extremes as that has also been one of my research areas and was the topic of my Ph.D. dissertation. This is the second outstanding book Resnick has written on extremes. This one has more of a modelling flavor to it with an eye toward financial applications. It seems these days that much of the research in time series modelling and stochastic processes is motivated by applications in finance. This is certainly also the case with extreme value models as can be seen by the many fine books on extremes that have appeared recently.

This book shows the theory and applications of models for heavy-tailed distributions. Resnick makes a very good point about insurance claim cost. This was certainly a phenomena I had to deal with when modeling workers compensation insurance claims at Risk Data Corporation. It is also interesting to see coverage about what is needed to consistently estimate extreme values by bootstrapping.

Time series models that deal with heavy-tailed distributions are also mentioned.

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advanced and abstract

The motivation for this book is simple. At least in the financial sector. Many models of financial phenomena use (or need) a probability distribution to model a range of events. Typically, there are a set of probable events, and then a long tail of unlikely events. But how unlikely? Resnick attempts to answer that here.

Where there is a chance of so-called heavy tail events. If these are not vanishingly unlikely in reality, then severe losses could be experienced by firms using the wrong model.

The text's analysis is quite advanced. Requiring extensive background in statistics and probability, and related aspects of modelling and queuing theory. An acquaintance with classical analysis (especially of metric spaces) is also needed, at the level of Marsden's treatment, Elementary Classical Analysis. The application to actual financial modelling is largely left to the reader. Those of you inclined to a quick perusal, to see if there are easy, immediate uses in finance, might have to spend considerable time digesting the text. And then doing research of your own.

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This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of many phenomena where the probability of a single huge value impacts heavily. Record-breaking insurance losses, financial-log returns, files sizes stored on a server, transmission rates of files are all examples of heavy-tailed phenomena.

Key features:

* Unique text devoted to heavy-tails

* Emphasizes both probability modeling and statistical methods for fitting models. Most treatments focus on one or the other but not both

* Presents broad applicability of heavy-tails to the fields of data networks, finance (e.g., value-at- risk), insurance, and hydrology

* Clear, efficient and coherent exposition, balancing theory and actual data to show the applicability and limitations of certain methods

* Examines in detail the mathematical properties of the methodologies as well as their implementation in Splus or R statistical languages

* Exposition driven by numerous examples and exercises

Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.

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