Guus Balkema (University of Amsterdam, The Netherlands)
Paul Embrechts (ETH Zurich, Switzerland)
September 2007, 388 pages, softcover, 17.0 cm x 24.0 cm.
ISBN 978-3-03719-035-7

Quantitative Risk Management (QRM) has become a field of research of considerable importance to numerous areas of application, including insurance, banking, energy, medicine, reliability. Mainly motivated by examples from insurance and finance, the authors develop a theory for handling multivariate extremes. The approach borrows ideas from portfolio theory and aims at an intuitive approach in the spirit of the Peaks over Thresholds method. The point of view is geometric. It leads to a probabilistic description of what in QRM language may be referred to as a high risk scenario: the conditional behaviour of risk factors given that a large move on a linear combination (portfolio, say) has been observed. The theoretical models which describe such conditional extremal behaviour are characterized and their relation to the limit theory for coordinatewise maxima is explained.

The first part is an elegant exposition of coordinatewise extreme value theory; the second half develops the more basic geometric theory. Besides a precise mathematical deduction of the main results, the text yields numerous discussions of a more applied nature. A twenty page preview introduces the key concepts; the extensive introduction provides links to financial mathematics and insurance theory.

The book is based on a graduate course on point processes and extremes. It could form the basis for an advanced course on multivariate extreme value theory or a course on mathematical issues underlying risk. Students in statistics and finance with a mathematical, quantitative background are the prime audience. Actuaries and risk managers involved in data based risk analysis will find the models discussed in the book stimulating. The text contains many indications for further research.

About this book:
This long-awaited book aims at a rigorous mathematical treatment of the theory of pricing and hedging of derivative securities by the principle of 'no arbitrage'. The first part presents a relatively elementary introduction, restricting itself to the case of finite probability spaces. The second part consists of an updated edition of seven original research papers by the authors, which analyse the topic in the general framework of semi-martingale theory.

Written for: 

Practitioners and researchers in mathematics, finance and economics

Keywords:

JEL: G12, G13
arbitrage, change of numeraire, fundamental theorem of asset pricing, martingale, superreplication

About this textbook:

The book is aimed at teachers and students as well as practising experts in the financial area, in particular at actuaries in the field of property-casualty insurance, life insurance, reinsurance and insurance supervision. Persons working in the wider world of finance will also find many relevant ideas and examples even though credibility methods have not yet been widely applied here.
The book covers the subject of Credibility Theory extensively and includes most aspects of this topic from the simplest case to the most general dynamic model. Credibility is a lifeless topic if it is not linked closely to practical applications. The book therefore treats explicitly the tasks which the actuary encounters in his daily work such as estimation of loss ratios, claim frequencies and claim sizes. This book deserves a place on the bookshelf of every actuary and mathematician who works, teaches or does research in the area of insurance and finance.

Written for:

Students and lecturers in mathematical finance, actuarial science, and Bayesian statistics

Keywords:

Bayesian statistics, actuarial science, financial modelling, insurance practice, quantitative finance

• A. J. McNeil,ETH Zürich, Switzerland
• R. Frey, University of Leipzig., Switzerland
• P. Embrechts,ETH Zürich, Switzerland

The implementation of sound quantitative risk models is a vital concern for all financial institutions, and this trend has accelerated in recent years with regulatory processes such as Basel II. This book provides a comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management and equips readers--whether financial risk analysts, actuaries, regulators, or students of quantitative finance--with practical tools to solve real-world problems. The authors cover methods for market, credit, and operational risk modelling; place standard industry approaches on a more formal footing; and describe recent developments that go beyond, and address main deficiencies of, current practice.

The book's methodology draws on diverse quantitative disciplines, from mathematical finance through statistics and econometrics to actuarial mathematics. Main concepts discussed include loss distributions, risk measures, and risk aggregation and allocation principles. A main theme is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. The techniques required derive from multivariate statistical analysis, financial time series modelling, copulas, and extreme value theory. A more technical chapter addresses credit derivatives. Based on courses taught to masters students and professionals, this book is a unique and fundamental reference that is set to become a standard in the field.

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Reference:
Wiley Finance, 2003, 396 pages. ISBN 0-470-84291-1

• Philipp J. Schönbucher, Department of Mathematics, ETH Zürich, Switzerland

The credit derivatives market is booming and, for the first time, expanding into the banking sector which previously has had very little exposure to quantitative modeling. This phenomenon has forced a large number of professionals to confront this issue for the first time. Credit Derivatives Pricing Models provides an extremely comprehensive overview of the most current areas in credit risk modeling as applied to the pricing of credit derivatives. As one of the first books to uniquely focus on pricing, this title is also an excellent complement to other books on the application of credit derivatives. Based on proven techniques that have been tested time and again, this comprehensive resource provides readers with the knowledge and guidance to effectively use credit derivatives pricing models. Filled with relevant examples that are applied to real-world pricing problems, Credit Derivatives Pricing Models paves a clear path for a better understanding of this complex issue.
Dr. Philippe J. Schonbucher is a professor at the University of Bonn, Germany, and has degrees in mathematics from Oxford University and a PhD in economics from Bonn University. He has taught various training courses organized by ICM and CIFT, and lectured at risk conferences for practitioners on credit derivatives pricing, credit risk modeling, and implementation.

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• Provides a comprehensive overview of extreme value theory
  from a financial perspective
• Expert academics examine the recent developments in the
  modelling of extremal events
• Offers an extension of traditional VAR methodologies and
  provides analysis of abnormal distribution at the end of the curve
• Examines the patterns and likelihood of the occurrence of
  extreme events
• Contributions selected and introduced by Professor Paul
  Embrechts, ETH Zürich

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Reference: May 2000, Risk Books, ISBN 1 899 332 89 8

• Provides an assessment of various models, examining the
  weaknesses and provides methods to mitigate potential model failures and
  deficiencies
• Covers the testing of models, what should be tested and
  what the parameters should be
• Core contributions selected and introduced by Professor
  Rajna Gibson, University of Zurich

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Errata

• P. Embrechts,ETH Zürich, Switzerland
• C. Klüppelberg,Technische Universität München, Germany
• T. Mikosch,University of Copenhagen, Denmark

Both in insurance and 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.

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Reference:
Princeton Series in Applied Mathematics,
Princeton University Press, Princeton and Oxford 2002, ISBN 0-691-09627-9

• Professor Paul Embrechts, Department of
  Mathematics, ETH Zürich,
  Switzerland
• Professor Makoto Maejima, Department
  of Mathematics, Keio University, Yokohama, Japan

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.