Martingales and Financial Mathematics in Discrete Time

Mathematics and Statistics for Financial Risk Management is a practical guide to modern financial risk management for both practitioners and academics. Now in its second edition with more topics, more sample problems and more real world examples, this popular guide to financial risk management introduces readers to practical quantitative techniques for analyzing and managing financial risk. In a concise and easy-to-read style, each chapter introduces a different topic in mathematics or statistics. As different techniques are introduced, sample problems and application sections demonstrate how these techniques can be applied to actual risk management problems. Exercises at the end of each chapter and the accompanying solutions at the end of the book allow readers to practice the techniques they are learning and monitor their progress. A companion Web site includes interactive Excel spreadsheet examples and templates. Mathematics and Statistics for Financial Risk Management is an indispensable reference for today’s financial risk professional.

Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.

Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.

Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. These two volumes aim to provide a foundation course on applied stochastic finance. They are designed for three groups of readers: firstly, students of various backgrounds seeking a core knowledge on the subject of stochastic finance; secondly financial analysts and practitioners in the investment, banking and insurance industries; and finally other professionals who are interested in learning advanced mathematical and stochastic methods, which are basic knowledge in many areas, through finance. Volume 1 starts with the introduction of the basic financial instruments and the fundamental principles of financial modeling and arbitrage valuation of derivatives. Next, we use the discrete-time binomial model to introduce all relevant concepts. The mathematical simplicity of the binomial model also provides us with the opportunity to introduce and discuss in depth concepts such as conditional expectations and martingales in discrete time. However, we do not expand beyond the needs of the stochastic finance framework. Numerous examples, each highlighted and isolated from the text for easy reference and identification, are included. The book concludes with the use of the binomial model to introduce interest rate models and the use of the Markov chain model to introduce credit risk. This volume is designed in such a way that, among other uses, makes it useful as an undergraduate course.

A whole is worth the sum of its parts. Even the most complex structured bond, credit arbitrage strategy or hedge trade can be broken down into its component parts, and if we understand the elemental components, we can then value the whole as the sum of its parts. We can quantify the risk that is hedged and the risk that is left as the residual exposure. If we learn to view all financial trades and securities as engineered packages of building blocks, then we can analyze in which structures some parts may be cheap and some may be rich. It is this relative value arbitrage principle that drives all modern trading and investment. This book is an easy-to-understand guide to the complex world of today’s financial markets teaching you what money and capital markets are about through a sequence of arbitrage-based numerical illustrations and exercises enriched with institutional detail. Filled with insights and real life examples from the trading floor, it is essential reading for anyone starting out in trading. Using a unique structural approach to teaching the mechanics of financial markets, the book dissects markets into their common building blocks: spot (cash), forward/futures, and contingent (options) transactions. After explaining how each of these is valued and settled, it exploits the structural uniformity across all markets to introduce the difficult subjects of financially engineered products and complex derivatives. The book avoids stochastic calculus in favour of numeric cash flow calculations, present value tables, and diagrams, explaining options, swaps and credit derivatives without any use of differential equations.

MATHEMATICS IN COMPUTATIONAL SCIENCE AND ENGINEERING This groundbreaking new volume, written by industry experts, is a must-have for engineers, scientists, and students across all engineering disciplines working in mathematics and computational science who want to stay abreast with the most current and provocative new trends in the industry. Applied science and engineering is the application of fundamental concepts and knowledge to design, build and maintain a product or a process, which provides a solution to a problem and fulfills a need. This book contains advanced topics in computational techniques across all the major engineering disciplines for undergraduate, postgraduate, doctoral and postdoctoral students. This will also be found useful for professionals in an industrial setting. It covers the most recent trends and issues in computational techniques and methodologies for applied sciences and engineering, production planning, and manufacturing systems. More importantly, it explores the application of computational techniques and simulations through mathematics in the field of engineering and the sciences. Whether for the veteran engineer, scientist, student, or other industry professional, this volume is a must-have for any library. Useful across all engineering disciplines, it is a multifactional tool that can be put to use immediately in practical applications. This groundbreaking new volume: Includes detailed theory with illustrations Uses an algorithmic approach for a unique learning experience Presents a brief summary consisting of concepts and formulae Is pedagogically designed to make learning highly effective and productive Is comprised of peer-reviewed articles written by leading scholars, researchers and professors [b]AUDIENCE: Engineers, scientists, students, researchers, and other professionals working in the field of computational science and mathematics across multiple disciplines

The term Financial Derivative is a very broad term which has come to mean any financial transaction whose value depends on the underlying value of the asset concerned. Sophisticated statistical modelling of derivatives enables practitioners in the banking industry to reduce financial risk and ultimately increase profits made from these transactions. The book originally published in March 2000 to widespread acclaim. This revised edition has been updated with minor corrections and new references, and now includes a chapter of exercises and solutions, enabling use as a course text. Comprehensive introduction to the theory and practice of financial derivatives. Discusses and elaborates on the theory of interest rate derivatives, an area of increasing interest. Divided into two self-contained parts ? the first concentrating on the theory of stochastic calculus, and the second describes in detail the pricing of a number of different derivatives in practice. Written by well respected academics with experience in the banking industry. A valuable text for practitioners in research departments of all banking and finance sectors. Academic researchers and graduate students working in mathematical finance.

A ground-breaking and practical treatment of probability and stochastic processes A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity. A Modern Theory of Random Variation is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation. Patrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.

There are many books covering Fibonacci from an artistic and historical point of view and almost as many suggesting that Fibonacci retracements and numbers can be successfully applied to financial market time series. What is missing is a book that addresses the common errors in using screen based Fibonacci (and Gann and other tools). The book is a critical exploration of Fibonacci numbers, retracements, projections, timeframes and fanlines and their current usage within the financial markets by technical analysts. Although they can be extremely effective analytical tools when used appropriately, mistakes in usage can be extremely costly from a financial and credibility viewpoint. George MacLean takes a brief look at the history of Fibonacci and Gann, before providing a full account of their applications in financial markets, including fixed income, equity, foreign exchange, commodities and indexes. In particular, he draws attention to the overuse and misuse of easily applied computer packages available to professional and amateur traders.