Alison Etheridge

Finance provides a dramatic example of the successful application of mathematics to the practical problem of pricing financial derivatives. This self-contained text is designed for first courses in financial calculus. Key concepts are introduced in the discrete time framework: proofs in the continuous-time world follow naturally. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts are applied to realistic financial questions.

Jon Lee

A First Course in Combinatorial Optimization is a self-contained text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. The author focuses on the key mathematical ideas that lead to useful models and algorithms rather than on data structures and implementation details. The viewpoint is polyhedral, and the author also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.

David Pollard

Rigorous probabilistic arguments, built on the foundation of measure theory introduced seventy years ago by Kolmogorov, have invaded many fields. Many students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students, who were expected only to have taken an undergraduate course in real analysis or advanced calculus.

Mark S. Joshi

This is the first book that combines the areas of mathematical finance, C++, and object-oriented programming (OOP). The author shows the relevance and use of OOP to financial mathematics by describing how to price derivatives to obtain reusable and extensible code. Much of the book is devoted to designing reusable components which are then combined to build a Monte Carlo pricer for exotic equity derivatives. Those who know the basics of C++ and mathematical finance, but are unclear how to use OOP to implement models, will welcome this account.

Stephen Boyd, Lieven Vandenberghe

Convex optimization problems arise frequently in many fields including circuit design, financial modelling, signal processing, networking and econometrics. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Sara A. van de Geer

This book deals with estimation methods in statistics, and treats various models in a unified way. Virtually all results are proved using only elementary ideas developed within the book; there is minimal recourse to abstract theoretical results. Many illustrative examples are given, including the Grenander estimator, estimation of functions of bounded variation, smoothing splines, partially linear models, mixture models and image analysis. Graduate students and professionals in statistics as well as those with an interest in applications, to such areas as econometrics, medical statistics, etc., will welcome this treatment.

Yuh-Dauh Lyuu

Combines the theory and mathematics behind financial engineering with an emphasis on computation, in keeping with the way financial engineering is practised in today's capital markets. It offers a thorough grounding in the subject for MBAs in finance, students of engineering and sciences who are pursuing a career in finance, researchers in computational finance, system analysts, and financial engineers. The author presents numerous algorithms for pricing, risk management, and portfolio management. The emphasis is on pricing financial and derivative securities: bonds, options, futures, forwards, interest rate derivatives, mortgage-backed securities, bonds with embedded options, and more. Each instrument is treated in a short, self-contained chapter for ready reference use. Many of these algorithms are coded in Java as programs for the Web, available from the book's home page.

Olle Häggström

Based on a lecture course given at Chalmers University of Technology, this book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory before applying it to study a range of randomised algorithms that have important applications in computing. This book will appeal not only to mathematicians, but to students of statistics and computer science who will find much here that appeals. The subject matter is introduced clearly and concisely and numerous exercises will help students to deepen their understanding.

Lakhdar Aggoun, Robert J. Elliott

Aimed primarily at those outside of the field of statistics, this book not only provides both an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion, but develops into an excellent users' guide to filtering. Includes exercises for students. This is a complete resource for engineers, signal processing researchers or indeed anyone with an interest in practical implementation of filtering techniques, in particular the Kalman filter. Three separate chapters concentrate on applications arising in finance, genetics and population modelling.

J. K. Lindsey

Many observed phenomena are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods for applying stochastic processes. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system, for the reader to apply to all the models presented.

Mark S. Joshi

For those starting out as practitioners of mathematical finance, this is an ideal introduction. It provides the reader with a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. There are plenty of worked examples and exercises, with answers, and many computer projects are supplied. The author brings to this book a blend of practical experience and rigorous mathematical background, and provides here the working knowledge needed to become a good quantitative analyst.

David Williams

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces Mathematics students of the intrinsic interest of Statistics and Probability, and Statistics students that the language of Mathematics can bring real insight and clarity to their subject. The presentation is enriched with examples drawn from all manner of applications. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Tests. C or WinBUGS code is provided for computational examples and simulations. Many exercises are included; hints or solutions are often provided.