The problem of heavy tails in many time series data, especially in finance, has long been present, bur researchers have not dedicated too much time to provide students and practitioners with sound solutions or partial solutions. There are only a few books and some research papers that deal with this phenomenon. Many calculations in finance are based on properties of the normal distribution, even when the data does not resemble the properties of a normal distribution but rather exhibit heavy tail phenomena. Reading and using this book will go a long way towards solving these problems.
Resnick's goal is to write a theoretical book on the problem of heavy tails. This is a serious exposition of the problem. It directly discusses the theoretical concepts behind the issues which are often hand-waved away by many practitioners when it comes to the calculations of for example Value-at-Risk and similar measures.
As already mentioned, the book is very technical; the prerequisites mentioned by the author are indeed necessary to efficiently grasp the text. Those prerequisites are stochastic processes, probability theory, time series analysis and some statistical background. I would just add that if these prerequisites are taken at the graduate or at least upper undergraduate level the reader would be most adequately prepared. Familiarity with R or S-Plus statistical software would be a plus.
The book is divided into three general parts covering introduction, probability and statistics. The introduction also includes a couple of crash courses on regular variation and weak convergence. Given the technicality of the book there is slight negligence on the intuitive presentation of the concepts. However, a good background knowledge of probability theory and stochastic processes can easily fill the gap.
Exercises are provided at the end of each chapter. Naturally all of the exercises are technical and proof based. Doing the exercises will greatly improve the understanding of the subject.
One of the biggest drawbacks of the book is the lack of examples. There are some small examples scattered throughout the book, but I believe this is not sufficient, especially since the book is intended for readers in finance. The author should have provided bigger scale examples with much more explanation. The book is suitable for graduate students in mathematical finance, finance, operations research and other similar fields. It should also be of great value to practitioners in finance provided they posses the appropriate background knowledge.
Ita Cirovic Donev is a PhD candidate at the University of Zagreb. She hold a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical mehods of credit and market risk. Apart from the academic work she does consulting work for financial institutions.
Introduction.- Part 1. Crash Courses.- Crash Course I: Regular Variation.- Crash Course II: Weak Convergence; Implications for Heavy Tail Analysis.- Part II. Statistics.- Dipping a Toe in the Statistical Water.- Part III. Probability.- The Poisson Process.- Multivariate Regular Variation and the Poisson Transform.- Weak Convergence and the Poisson Process.- Applied Probability Models and Heavy Tails.- Part IV. More Statistics.-Additional Statistics Topics.- Part V. Appendices.- Notation and Conventions.- Software Routines.- Index.