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Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance
Stochastic finance and financial engineering have been rapidlyexpanding fields of science over the past four decades, mainly dueto the success of sophisticated quantitative methodologies inhelping professionals manage financial risks. In recent years, wehave witnessed a tremendous acceleration in research efforts aimedat better comprehending, modeling and hedging this kind ofrisk. These two volumes aim to provide a foundation course on appliedstochastic finance. They are designed for three groups of readers:firstly, students of various backgrounds seeking a core knowledgeon the subject of stochastic finance; secondly financial analystsand practitioners in the investment, banking and insuranceindustries; and finally other professionals who are interested inlearning advanced mathematical and stochastic methods, which arebasic knowledge in many areas, through finance. Volume 1 starts with the introduction of the basic financialinstruments and the fundamental principles of financial modelingand arbitrage valuation of derivatives. Next, we use thediscrete-time binomial model to introduce all relevant concepts.The mathematical simplicity of the binomial model also provides uswith the opportunity to introduce and discuss in depth conceptssuch as conditional expectations and martingales in discrete time.However, we do not expand beyond the needs of the stochasticfinance framework. Numerous examples, each highlighted and isolatedfrom the text for easy reference and identification, areincluded. The book concludes with the use of the binomial model tointroduce interest rate models and the use of the Markov chainmodel to introduce credit risk. This volume is designed in such away that, among other uses, makes it useful as an undergraduatecourse.
An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models. The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features: A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.
"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM
Capitalize on All the Latest Legal, Financial, and Compliance Information Needed to Analyze and Appraise Any Business For over 25 years, Valuing a Business has provided professionals and students with expert business valuation information, offering clear, concise coverage of valuation principles and methods. Over the decades, the book's unsurpassed explanations of all valuation issues have made it the definitive text in the field, against which every other business valuation book is measured. Now updated with new legal, financial, and compliance material, the Fifth Edition of Valuing a Business presents detailed answers to virtually all valuation questions_ranging from executive compensation and lost profits analysis...to ESOP issues and valuation discounts. Written by Shannon Pratt, one of the world's leading authorities on business valuation, this updated classic offers a complete “one-stop” compendium of information on the full range of valuation concepts and methods. Valuing a Business contains step-by-step discussions and analyses of: Business Valuation Standards and Credentials Defining the Assignment Business Valuation Theory and Principles Gathering Company Data Site Visits and Interviews Researching Economic and Industry Information Analyzing Financial Statements Financial Statement Ratio Analysis Income, Market, and Asset-Based Approaches to Valuation The Capitalized Excess Earnings Method Premiums and Discounts Writing and Reviewing Business Valuation Reports Valuing Debt Securities, Preferred Stock, Stock Options, and S Corporation Stock Valuations for Estate and Gift Tax Purposes Buy-Sell Agreements Valuations for Income Tax Purposes Valuation with Employee Stock Ownership Plans Valuations for Ad Valorem Taxation Dissenting Stockholder and Minority Oppression Actions Valuations for Marital Dissolution Purposes Litigation Support Services Expert Testimony Arbitration and Mediation This landmark reference also presents a wealth of recent court cases for each valuation area, which together provide a comprehensive overview of all the legal rulings and trends in the field of business valuation.
This book deals with many topics in modern financial mathematics in a way that does not use advanced mathematical tools and shows how these models can be numerically implemented in a practical way. The book is aimed at undergraduate students, MBA students, and executives who wish to understand and apply financial models in the spreadsheet computing environment. The basic building block is the one-step binomial model where a known price today can take one of two possible values at the next time. In this simple situation, risk neutral pricing can be defined and the model can be applied to price forward contracts, exchange rate contracts, and interest rate derivatives. The simple one-period framework can then be extended to multi-period models. The authors show how binomial tree models can be constructed for several applications to bring about valuations consistent with market prices. The book closes with a novel discussion of real options. John van der Hoek is Senior Lecturer in Applied Mathematics at the University of Adelaide. He has developed courses in finance for a number of years at various levels and is a regular plenary speaker at major conferences on Quantitative Finance. Robert J. Elliott is RBC Financial Group Professor of Finance at the Haskayne School of Business at the University of Calgary. He is the author of over 300 research papers and several books, including Mathematics of Financial Markets, Second Edition (with P. Ekkehard Kopp), Stochastic Calculus and Applications, Hidden Markov Models (with Lahkdar Aggoun and John Moore) and Measure Theory and Filtering: Theory and Applications (with Lakhdar Aggoun). He is an Associate Editor of Mathematical Finance, Stochastics and Stochastics Reports, Stochastic Analysis and Applications, and the Canadian Applied Mathematics Quarterly.
This book presents the mathematics that underpins pricing models for derivative securities in modern financial markets, such as options, futures and swaps. This new edition adds substantial material from current areas of active research, such as coherent risk measures with applications to hedging, the arbitrage interval for incomplete discrete-time markets, and risk and return and sensitivity analysis for the Black-Scholes model.

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