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Applied Mathematics for Personal Finance provides a general introduction to the ways that mathematics can be applied to personal financial decision-making. This book is suitable for college students with no previous background in economics or finance; only familiarity with high school algebra is assumed.This book demonstrates how you can utilize math skills you already know in application areas that may be unfamiliar; it also introduces some new math skills that you can apply to familiar problems. The book emphasizes the development and application of the economic life-cycle model as the framework for evaluating all of your personal financial decisions. Economists, including six Nobel Laureates, have spent close to a century developing the concept of life-cycle consumption smoothing. “Smoothing” refers to the need to spread your economic resources over your lifetime, taking into account that your future is highly uncertain.
"Master everything from banking and loan interest to budgets and business costs"--Cover.
Glencoe’s Mathematics for Business and Personal Finance is the only text on the market that offers teachers point-of-use online professional development, interactive online help for students and the option of purchasing an interactive online text with a grade book. As always, we have maintained our exclusive coverage of key core academic content, and our research-based reading strategies.
This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion- driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text. This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options. Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8.
The second edition of this successful and widely recognized textbook again focuses on discrete topics. The author recognizes two distinct paths of study and careers of actuarial science and financial engineering. This text can be very useful as a common core for both. Therefore, there is substantial material on the theory of interest (the first half of the book), as well as the probabilistic background necessary for the study of portfolio optimization and derivative valuation (the second half). The material in the first two chapters should go a long way toward helping students prepare for the Financial Mathematics (FM) actuarial exam. Also, the discrete material will reveal how beneficial it is to know more about loans in student's personal financial lives. The notable changes and updates to this edition are itemized in the Preface, however, overall, the presentation has been made more efficient. One example is the chapter on discrete probability, rather unique in its emphasis on giving the deterministic problems studied earlier a probabilistic context. Probably is now a subsection on Markov chains. Sample spaces and probability measures, random variables and distributions, expectation, conditional probability, independence, and estimation all follow. Optimal portfolio selection coverage is reorganized and the section on the practicalities of stock transactions has been revised. Market portfolio, and Capital Market Theory coverage is expanded. This book, like the first edition, was written so that the print edition could stand alone. At times we simplify complicated algebraic expressions, or solve systems of linear equations, or numerically solve non-linear equations. Also, some attention is given to the use of computer simulation to approximate solutions to problems. A course in multivariable calculus is not required. The entire text is available digitally from the publisher in the form of a series of Mathematica notebooks, which can be loaded into Mathematica, and which include complete executable commands and programs, and some additional material.
A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.
The second edition of a successful text providing the working knowledge needed to become a good quantitative analyst. An ideal introduction to mathematical finance, readers will gain a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice.
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 the mathematical skills needed to understand finance and make better financial decisions Mathematical Finance enables readers to develop the mathematical skills needed to better understand and solve financial problems that arise in business, from small entrepreneurial operations to large corporations, and to also make better personal financial decisions. Despite the availability of automated tools to perform financial calculations, the author demonstrates that a basic grasp of the underlying mathematical formulas and tables is essential to truly understand finance. The book begins with an introduction to the most fundamental mathematical concepts, including numbers, exponents, and logarithms; mathematical progressions; and statistical measures. Next, the author explores the mathematics of the time value of money through a discussion of simple interest, bank discount, compound interest, and annuities. Subsequent chapters explore the mathematical aspects of various financial scenarios, including: Mortgage debt, leasing, and credit and loans Capital budgeting, depreciation, and depletion Break-even analysis and leverage Investing, with coverage of stocks, bonds, mutual funds, options, cost of capital, and ratio analysis Return and risk, along with a discussion of the Capital Asset Pricing Model (CAPM) Life annuities as well as life, property, and casualty insurance Throughout the book, numerous examples and exercises present realistic financial scenarios that aid readers in applying their newfound mathematical skills to devise solutions. The author does not promote the use of financial calculators and computers, but rather guides readers through problem solving using formulas and tables with little emphasis on derivations and proofs. Extensively class-tested to ensure an easy-to-follow presentation, Mathematical Finance is an excellent book for courses in business, economics, and mathematics of finance at the upper-undergraduate and graduate levels. The book is also appropriate for consumers and entrepreneurs who need to build their mathematical skills in order to better understand financial problems and make better financial choices.
The new edition of this influential textbook, geared towards graduate or advanced undergraduate students, teaches the statistics necessary for financial engineering. In doing so, it illustrates concepts using financial markets and economic data, R Labs with real-data exercises, and graphical and analytic methods for modeling and diagnosing modeling errors. These methods are critical because financial engineers now have access to enormous quantities of data. To make use of this data, the powerful methods in this book for working with quantitative information, particularly about volatility and risks, are essential. Strengths of this fully-revised edition include major additions to the R code and the advanced topics covered. Individual chapters cover, among other topics, multivariate distributions, copulas, Bayesian computations, risk management, and cointegration. Suggested prerequisites are basic knowledge of statistics and probability, matrices and linear algebra, and calculus. There is an appendix on probability, statistics and linear algebra. Practicing financial engineers will also find this book of interest.