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An Introduction to the Mathematics of Finance

An Introduction to the Mathematics of Finance
  • Author : Stephen Garrett
  • Publisher :Unknown
  • Release Date :2013-05-28
  • Total pages :464
  • ISBN : 9780080982755
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Summary : An Introduction to the Mathematics of Finance: A Deterministic Approach, 2e, offers a highly illustrated introduction to mathematical finance, with a special emphasis on interest rates. This revision of the McCutcheon-Scott classic follows the core subjects covered by the first professional exam required of UK actuaries, the CT1 exam. It realigns the table of contents with the CT1 exam and includes sample questions from past exams of both The Actuarial Profession and the CFA Institute. With a wealth of solved problems and interesting applications, An Introduction to the Mathematics of Finance stands alone in its ability to address the needs of its primary target audience, the actuarial student. Closely follows the syllabus for the CT1 exam of The Institute and Faculty of Actuaries Features new content and more examples Online supplements available: http://booksite.elsevier.com/9780080982403/ Includes past exam questions from The Institute and Faculty of Actuaries and the CFA Institute

Introduction to the Mathematics of Finance

Introduction to the Mathematics of Finance
  • Author : Steven Roman
  • Publisher :Unknown
  • Release Date :2013-12-01
  • Total pages :356
  • ISBN : 9781441990051
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Summary : An elementary introduction to probability and mathematical finance including a chapter on the Capital Asset Pricing Model (CAPM), a topic that is very popular among practitioners and economists. Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag.

Introduction to the Mathematics of Finance

Introduction to the Mathematics of Finance
  • Author : Steven Roman
  • Publisher :Unknown
  • Release Date :2012-04-24
  • Total pages :288
  • ISBN : 9781461435822
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Summary : The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options.

Introduction to the Mathematics of Finance

Introduction to the Mathematics of Finance
  • Author : Ruth J. Williams
  • Publisher :Unknown
  • Release Date :2006
  • Total pages :150
  • ISBN : 9780821839034
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Summary : The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions.

An Introduction to the Mathematics of Financial Derivatives

An Introduction to the Mathematics of Financial Derivatives
  • Author : Salih N. Neftci,Ali Hirsa,Salih N.. Neftci
  • Publisher :Unknown
  • Release Date :2000-06-02
  • Total pages :527
  • ISBN : 9780125153928
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Summary : A step-by-step explanation of the mathematical models used to price derivatives. For this second edition, Salih Neftci has expanded one chapter, added six new ones, and inserted chapter-concluding exercises. He does not assume that the reader has a thorough mathematical background. His explanations of financial calculus seek to be simple and perceptive.

Mathematics for Finance

Mathematics for Finance
  • Author : Marek Capinski,Tomasz Zastawniak
  • Publisher :Unknown
  • Release Date :2006-04-18
  • Total pages :314
  • ISBN : 9781852338466
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Summary : This textbook contains the fundamentals for an undergraduate course in mathematical finance aimed primarily at students of mathematics. Assuming only a basic knowledge of probability and calculus, the material is presented in a mathematically rigorous and complete way. The book covers the time value of money, including the time structure of interest rates, bonds and stock valuation; derivative securities (futures, options), modelling in discrete time, pricing and hedging, and many other core topics. With numerous examples, problems and exercises, this book is ideally suited for independent study.

An Introduction to Mathematical Finance with Applications

An Introduction to Mathematical Finance with Applications
  • Author : Arlie O. Petters,Xiaoying Dong
  • Publisher :Unknown
  • Release Date :2016-06-17
  • Total pages :483
  • ISBN : 9781493937837
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Summary : This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.

An Undergraduate Introduction to Financial Mathematics

An Undergraduate Introduction to Financial Mathematics
  • Author : J Robert Buchanan
  • Publisher :Unknown
  • Release Date :2008-09-29
  • Total pages :372
  • ISBN : 9789814365321
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Summary : This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses. It introduces the Theory of Interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. The reader progresses from a solid grounding in multi-variable calculus through a derivation of the Black–Scholes equation, its solution, properties, and applications.

Understanding the Mathematics of Personal Finance

Understanding the Mathematics of Personal Finance
  • Author : Lawrence N. Dworsky
  • Publisher :Unknown
  • Release Date :2009-09-22
  • Total pages :288
  • ISBN : 0470538384
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Summary : A user-friendly presentation of the essential concepts and tools for calculating real costs and profits in personal finance Understanding the Mathematics of Personal Finance explains how mathematics, a simple calculator, and basic computer spreadsheets can be used to break down and understand even the most complex loan structures. In an easy-to-follow style, the book clearly explains the workings of basic financial calculations, captures the concepts behind loans and interest in a step-by-step manner, and details how these steps can be implemented for practical purposes. Rather than simply providing investment and borrowing strategies, the author successfully equips readers with the skills needed to make accurate and effective decisions in all aspects of personal finance ventures, including mortgages, annuities, life insurance, and credit card debt. The book begins with a primer on mathematics, covering the basics of arithmetic operations and notations, and proceeds to explore the concepts of interest, simple interest, and compound interest. Subsequent chapters illustrate the application of these concepts to common types of personal finance exchanges, including: Loan amortization and savings Mortgages, reverse mortgages, and viatical settlements Prepayment penalties Credit cards The book provides readers with the tools needed to calculate real costs and profits using various financial instruments. Mathematically inclined readers will enjoy the inclusion of mathematical derivations, but these sections are visually distinct from the text and can be skipped without the loss of content or complete understanding of the material. In addition, references to online calculators and instructions for building the calculations involved in a spreadsheet are provided. Furthermore, a related Web site features additional problem sets, the spreadsheet calculators that are referenced and used throughout the book, and links to various other financial calculators. Understanding the Mathematics of Personal Finance is an excellent book for finance courses at the undergraduate level. It is also an essential reference for individuals who are interested in learning how to make effective financial decisions in their everyday lives.

An Introduction to Financial Mathematics

An Introduction to Financial Mathematics
  • Author : Hugo D. Junghenn
  • Publisher :Unknown
  • Release Date :2019-03-14
  • Total pages :304
  • ISBN : 9780429558962
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Summary : Introduction to Financial Mathematics: Option Valuation, Second Edition is a well-rounded primer to the mathematics and models used in the valuation of financial derivatives. The book consists of fifteen chapters, the first ten of which develop option valuation techniques in discrete time, the last five describing the theory in continuous time. The first half of the textbook develops basic finance and probability. The author then treats the binomial model as the primary example of discrete-time option valuation. The final part of the textbook examines the Black-Scholes model. The book is written to provide a straightforward account of the principles of option pricing and examines these principles in detail using standard discrete and stochastic calculus models. Additionally, the second edition has new exercises and examples, and includes many tables and graphs generated by over 30 MS Excel VBA modules available on the author’s webpage https://home.gwu.edu/~hdj/.

Mathematics of Finance

Mathematics of Finance
  • Author : Donald G. Saari
  • Publisher :Unknown
  • Release Date :2019-08-31
  • Total pages :144
  • ISBN : 9783030254438
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Summary : This textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools. Financial interactions are characterized by a vast amount of data and uncertainty; navigating the inherent dangers and hidden opportunities requires a keen understanding of what techniques to apply and when. By exploring the conceptual foundations of options pricing, the author equips readers to choose their tools with a critical eye and adapt to emerging challenges. Introducing the basics of gambles through realistic scenarios, the text goes on to build the core financial techniques of Puts, Calls, hedging, and arbitrage. Chapters on modeling and probability lead into the centerpiece: the Black–Scholes equation. Omitting the mechanics of solving Black–Scholes itself, the presentation instead focuses on an in-depth analysis of its derivation and solutions. Advanced topics that follow include the Greeks, American options, and embellishments. Throughout, the author presents topics in an engaging conversational style. “Intuition breaks” frequently prompt students to set aside mathematical details and think critically about the relevance of tools in context. Mathematics of Finance is ideal for undergraduates from a variety of backgrounds, including mathematics, economics, statistics, data science, and computer science. Students should have experience with the standard calculus sequence, as well as a familiarity with differential equations and probability. No financial expertise is assumed of student or instructor; in fact, the text’s deep connection to mathematical ideas makes it suitable for a math capstone course. A complete set of the author’s lecture videos is available on YouTube, providing a comprehensive supplementary resource for a course or independent study.

An Introduction to the Mathematics of Finance

An Introduction to the Mathematics of Finance
  • Author : Alfred Hurlstone Pollard
  • Publisher :Unknown
  • Release Date :1977
  • Total pages :93
  • ISBN : 0080217966
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Summary : An Introduction to the Mathematics of Finance provides a simple, nonmathematical introduction to the mathematics of finance. Topics discussed in this book include simple interest; compound interest-annual compounding; annuities-certain; use of compound interest; and sinking funds. The equations of value; compounding more frequently than annually; and contracts at """"flat"""" rates of interest are also deliberated. This text likewise elaborates on the loans repayable by equal annual installments when interest is charged only on the amount of principal from time to time outstanding. Exercises a...

Introduction to the Economics and Mathematics of Financial Markets

Introduction to the Economics and Mathematics of Financial Markets
  • Author : Jakša Cvitanić,Fernando Zapatero
  • Publisher :Unknown
  • Release Date :2004
  • Total pages :494
  • ISBN : 0262033208
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Summary : An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models--a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.

An Introduction to the Mathematics of Finance

An Introduction to the Mathematics of Finance
  • Author : John J. McCutcheon,William F. Scott
  • Publisher :Unknown
  • Release Date :1986-01-01
  • Total pages :463
  • ISBN : 0750603887
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Summary : In today's money markets interest rates are all-important. This book, which is intended as a successor to D.W.A Donald's Compound Interest and Annuities-certain, develops the classical theory of compound interest (in which the force of interest is constant) as a special case of a more general model. There is a concise but thorough treatment of the basic compound interest functions, nominal rate of interest, and the yield (or internal rate of return) and there are many examples on discounted cash flow. Also discussed are applications of the theory to capital redemption policies (with allowance for income tax, capital gains tax and index-linking), and consumer credit calculations. The final chapter provides a simple introduction to stochastic interest rate models. Concise and thorough Extensive use of examples Endorsed by the Institute of Actuaries and the Faculty of Actuaries

The Financial Mathematics of Market Liquidity

The Financial Mathematics of Market Liquidity
  • Author : Olivier Gueant
  • Publisher :Unknown
  • Release Date :2016-03-30
  • Total pages :302
  • ISBN : 9781498725484
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Summary : This book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problems-inspired from the Almgren-Chriss app

An Introduction to Financial Option Valuation

An Introduction to Financial Option Valuation
  • Author : Desmond J. Higham
  • Publisher :Unknown
  • Release Date :2004-04-15
  • Total pages :273
  • ISBN : 0521547571
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Summary : This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.

Financial Mathematics

Financial Mathematics
  • Author : Giuseppe Campolieti,Roman N. Makarov
  • Publisher :Unknown
  • Release Date :2018-10-24
  • Total pages :829
  • ISBN : 9781315360485
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Summary : Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors’ teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones. Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.

Stochastic Finance

Stochastic Finance
  • Author : Hans Föllmer,Alexander Schied
  • Publisher :Unknown
  • Release Date :2016-07-25
  • Total pages :608
  • ISBN : 9783110463453
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Summary : This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures

Financial Calculus

Financial Calculus
  • Author : Martin Baxter,Andrew Rennie
  • Publisher :Unknown
  • Release Date :1996-09-19
  • Total pages :229
  • ISBN : 9781139643276
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Summary : The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided. This unique book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders.

Financial Products

Financial Products
  • Author : Bill Dalton
  • Publisher :Unknown
  • Release Date :2008-10-02
  • Total pages :408
  • ISBN : 1139474057
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Summary : Financial Products provides a step-by-step guide to some of the most important ideas in financial mathematics. It describes and explains interest rates, discounting, arbitrage, risk neutral probabilities, forward contracts, futures, bonds, FRA and swaps. It shows how to construct both elementary and complex (Libor) zero curves. Options are described, illustrated and then priced using the Black Scholes formula and binomial trees. Finally, there is a chapter describing default probabilities, credit ratings and credit derivatives (CDS, TRS, CSO and CDO). An important feature of the book is that it explains this range of concepts and techniques in a way that can be understood by those with only a basic understanding of algebra. Many of the calculations are illustrated using Excel spreadsheets, as are some of the more complex algebraic processes. This accessible approach makes it an ideal introduction to financial products for undergraduates and those studying for professional financial qualifications.

The Mathematics of Financial Derivatives

The Mathematics of Financial Derivatives
  • Author : Paul Wilmott,Susan Howson,Sam Howison,Wilmott-Howison-Dewynne ...,Jeff Dewynne
  • Publisher :Unknown
  • Release Date :1995-09-29
  • Total pages :317
  • ISBN : 0521497892
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Summary : Basic option theory - Numerical methods - Further option theory - Interest rate derivative products.