Modelling Extremal Events for Insurance and Finance (Applications of Mathematics)

Book 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.


Book Info
Presents a comprehensive treatment of extreme value methodology for random walk models, time series, certain type of continuous-time stochastic processes and compound Poisson processes, all standard models which occur in applications in mathematical finance.


From the Publisher
Mathematical Reviews /MathSciNet database, R. A. Maller. 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... a worthwhile book in an extremely important area. SIAM Review, Roger Pinkham, Stevens Institute of Technology. [...] 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, Casper de Vries (Erasmus University, Rotterdam). The book is the first in the area that strikes a proper balance between mathematical rigor and scope on the probability side, and the statistically oriented applications for the practitioner. [...] The authors mostly rely on financially oriented examples, but the coverage of methods is such that anyone using extreme value technique should consult the book. [...] It is an exceptional book, recommended to practitioners, students and researchers alike. Mathematics Today, Mark H. Robson (Bank of England). This large, recently published volume has already established itself as the indispensable starting point for anyone interested in contemporary applications and extensions of classical extreme value theory. Extremes, Anders Martin-Löf (Stockholm University). 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, Ragnar Norberg (London School of Economics). This long-awaited volume gathers and systematizes a huge material, parts of which were hitherto scattered around in journals. [...] Given the nature of the subject, which is highly technical, 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, with ample illustrations (100 figures) and discussions of authentic cases and data. An amazing amount of knowledge, also on the practical side, is generously shared with the readers here. Mathematical rigour is never compromised, but is still exercised in measured amounts; proofs are given when they serve an educative purpose, and adequate references are given otherwise. The list of 646 references opens virtually unlimited access to supplementary reading.


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