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Ideal for college students in intermediate finance courses, this book uniquely applies mathematical formulas to teach the underpinnings of financial and lending decisions, covering common applications in real estate, capital budgeting, and commercial loans. An updated and expanded version of the time-honored classic text on financial math, this book provides, in one place, a complete and practical treatment of the four primary venues for finance: commercial lending, financial formulas, mortgage lending, and resource allocation or capital budgeting techniques. With an emphasis on understanding the principles involved rather than blind reliance on formulas, the book provides rigorous and thorough explanations of the mathematical calculations used in determining the time value of money, valuation of loans by commercial banks, valuation of mortgages, and the cost of capital and capital budgeting techniques for single as well as mutually exclusive projects. This new edition devotes an entire chapter to a method of evaluating mutually exclusive projects without resorting to any imposed conditions. Two chapters not found in the previous edition address special topics in finance, including a novel and innovative way to approach amortization tables and the time value of money for cash flows when they increase geometrically or arithmetically. This new edition also features helpful how-to sections on Excel applications at the end of each appropriate chapter.
Financial and insurance calculations become more and more frequent and helpful for many users not only in their profession life but sometimes even in their personal life. Therefore a survey of formulas of ?nancial and insurance mathematics that can be applied to such calculations seems to be a suitable aid. In some cases one should use instead of the term formula more suitable terms of the type method, p- cedure or algorithm since the corresponding calculations cannot be simply summed up to a single expression, and a verbal description without introducing complicated symbols is more appropriate. The survey has the following ambitions: • The formulas should be applicable in practice: it has motivated their choice for this survey ?rst and foremost. On the other hand it is obvious that by time one puts to use in practice seemingly very abstract formulas of higher mathematics, e.g. when pricing ?nancial derivatives, evaluating ?nancial risks, applying accou- ing principles based on fair values, choosing alternative risk transfers ARL in insurance, and the like. • The formulas should be error-free (though such a goal is not achievable in full) since in the ?nancial and insurance framework one publishes sometimes in a h- tic way various untried formulas and methods that may be incorrect. Of course, the formulas are introduced here without proofs because their derivation is not the task of this survey.
Mathematics for Financial Analysis focuses on the application of mathematics in financial analysis, including applications of differentiation, logarithmic functions, and compounding. The publication first ponders on equations and graphs, vectors and matrices, and linear programming. Discussions focus on duality and minimization problems, systems of linear inequalities, linear programs, matrix inversion, properties of matrices and vectors, vector products, equations and graphs, higher dimensional spaces, distance in the plane, coordinate geometry, and inequalities and absolute value. The text then examines differential calculus, applications of differentiation, and antidifferentiation and definite integration. Topics include fundamental theorem of calculus, definite integral, profit optimization in a monopoly, revenue from taxation, curve sketching, concavity and points of inflection, and rules for differentiation. The book examines the applications of integration and differentiation and integration of exponential and logarithmic functions, including exponential and logarithmic functions, differentiation and integration of logarithmic functions, and continuous compounding. The publication is a valuable source of data for researchers interested in the application of mathematics in financial analysis.
This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the book has real-world applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. It is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering.
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.
This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.
Credit Scoring and Its Applications is recognized as the bible of credit scoring. It contains a comprehensive review of the objectives, methods, and practical implementation of credit and behavioral scoring. The authors review principles of the statistical and operations research methods used in building scorecards, as well as the advantages and disadvantages of each approach. The book contains a description of practical problems encountered in building, using, and monitoring scorecards and examines some of the country-specific issues in bankruptcy, equal opportunities, and privacy legislation. It contains a discussion of economic theories of consumers' use of credit, and readers will gain an understanding of what lending institutions seek to achieve by using credit scoring and the changes in their objectives. New to the second edition are lessons that can be learned for operations research model building from the global financial crisis, current applications of scoring, discussions on the Basel Accords and their requirements for scoring, new methods for scorecard building and new expanded sections on ways of measuring scorecard performance. And survival analysis for credit scoring. Other unique features include methods of monitoring scorecards and deciding when to update them, as well as different applications of scoring, including direct marketing, profit scoring, tax inspection, prisoner release, and payment of fines.
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