Paul Embrechts

"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...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." --MATHEMATICAL REVIEWS

The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications.After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications.Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.

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.

Explore risk through numerous examples and their statistical modeling, travelling from a historical perspective all the way to an up-to-date technical analysis. Written with a wide readership in mind, this book begins with accounts of select major historical disasters, such as the North Sea Flood of 1953 and the L'Aquila earthquake. These tales serve to set the scene and to motivate the second part of the book, which describes the mathematical tools required to analyze these events, and how to use them. The focus is on the basic understanding of the mathematical modeling of risk and what types of questions the methods allow us to answer. The text offers a bridge between the world of science and that of everyday experience. It is written to be accessible to readers with only a basic background in mathematics and statistics. Even the more technical discussions are interspersed with historical comments and plentiful examples.

"This is the International Edition. The content is in English, same as US version but different cover. Please DO NOT buy if you can not accept this difference. Ship from Shanghai China, please allow about 3 weeks on the way to US or Europe. Message me if you have any questions."