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Extreme Value Theory and Applications
It appears that we live in an age of disasters: the mighty Missis sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening. While all these may seem to be unexpected phenomena to the man on the street, they are actually happening according to well defined rules of science known as extreme value theory. We know that records must be broken in the future, so if a flood design is based on the worst case of the past then we are not really prepared against floods. Materials will fail due to fatigue, so if the body of an aircraft looks fine to th...
A Course on Point Processes
This graduate-level textbook provides a straight-forward and mathematically rigorous introduction to the standard theory of point processes. The author's aim is to present an account which concentrates on the essentials and which places an emphasis on conveying an intuitive understanding of the subject. As a result, it provides a clear presentation of how statistical ideas can be viewed from this perspective and particular topics covered include the theory of extreme values and sampling from finite populations. Prerequisites are that the reader has a basic grounding in the mathematical theory of probability and statistics, but otherwise the book is self-contained. It arises from courses given by the author over a number of years and includes numerous exercises ranging from simple computations to more challenging explorations of ideas from the text.
The Novikov Conjecture
These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.
Operational Risk
This paper investigates the generalized parametric measurement methods of aggregate operational risk in compliance with the regulatory capital standards for operational risk in the New Basel Capital Accord ("Basel II"). Operational risk is commonly defined as the risk of loss resulting from inadequate or failed internal processes and information systems, from misconduct by people or from unforeseen external events. Our analysis informs an integrated assessment of the quantification of operational risk exposure and the consistency of current capital rules on operational risk based on generalized parametric estimation.
Advances in Mathematical and Statistical Modeling
Enrique Castillo is a leading figure in several mathematical and engineering fields. Organized to honor Castillo’s significant contributions, this volume is an outgrowth of the "International Conference on Mathematical and Statistical Modeling," and covers recent advances in the field. Applications to safety, reliability and life-testing, financial modeling, quality control, general inference, as well as neural networks and computational techniques are presented.
Numerical Methods for Finance
Featuring international contributors from both industry and academia, Numerical Methods for Finance explores new and relevant numerical methods for the solution of practical problems in finance. It is one of the few books entirely devoted to numerical methods as applied to the financial field. Presenting state-of-the-art methods in this area
XploRe — Learning Guide
It is generally accepted that training in statistics must include some exposure to the mechanics of computational statistics. This learning guide is intended for beginners in computer-aided statistical data analysis. The prerequisites for XploRe - the statistical computing environment - are an introductory course in statistics or mathematics. The reader of this book should be familiar with basic elements of matrix algebra and the use of HTML browsers. This guide is designed to help students to XploRe their data, to learn (via data interaction) about statistical methods and to disseminate their findings via the HTML outlet. The XploRe APSS (Auto Pilot Support System) is a powerful tool for fi...
Computational Statistics
Suitable for a compact course or self-study, Computational Statistics: An Introduction to R illustrates how to use the freely available R software package for data analysis, statistical programming, and graphics. Integrating R code and examples throughout, the text only requires basic knowledge of statistics and computing. This introduction covers one-sample analysis and distribution diagnostics, regression, two-sample problems and comparison of distributions, and multivariate analysis. It uses a range of examples to demonstrate how R can be employed to tackle statistical problems. In addition, the handy appendix includes a collection of R language elements and functions, serving as a quick reference and starting point to access the rich information that comes bundled with R. Accessible to a broad audience, this book explores key topics in data analysis, regression, statistical distributions, and multivariate statistics. Full of examples and with a color insert, it helps readers become familiar with R.
Laws of Small Numbers: Extremes and Rare Events
Since the publication of the first edition of this seminar book, the theory and applications of extremes and rare events have seen increasing interest. Laws of Small Numbers gives a mathematically oriented development of the theory of rare events underlying various applications. The new edition incorporates numerous new results on about 130 additional pages. Part II, added in the second edition, discusses recent developments in multivariate extreme value theory.
From Statistics to Mathematical Finance
This book, dedicated to Winfried Stute on the occasion of his 70th birthday, presents a unique collection of contributions by leading experts in statistics, stochastic processes, mathematical finance and insurance. The individual chapters cover a wide variety of topics ranging from nonparametric estimation, regression modelling and asymptotic bounds for estimators, to shot-noise processes in finance, option pricing and volatility modelling. The book also features review articles, e.g. on survival analysis.
