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• Theory of Interest Rate of Return and Present Value Compound Interest Annuities Loans Measuring Rate of Return Continuous Time Interest Theory Bonds Bond Valuation More on Bonds Term Structure of Interest Rates Discrete Probability for Finance Sample Spaces and Probability Measures Random Variables and Distributions Discrete Expectation Conditional Probability Independence and Dependence Estimation and Simulation Portfolio Theory Stocks Portfolios of Risky Assets Optimal Portfolio Selection Valuation of Derivatives Basic Terminology and Ideas Single-Period Options Multiple-Period Options Valuation of Exotic Options and Simulation Appendix: Answers to Selected Exercises Bibliography Index.
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Introduction to Financial Mathematics is ideal for an introductory undergraduate course. Unlike most textbooks aimed at more advanced courses, the text motivates students through a discussion of personal finances and portfolio management. The author then goes on to cover valuation of financial derivatives in discrete time, using all of closed form, recursive, and simulation methods. The text covers nearly all of the syllabus topics of the Financial Mathematics Actuarial examination, providing students with the foundation they require for future studies and throughout their careers. It begins by covering standard material on the mathematics of interest, including compound interest, present value, annuities, loans, several versions of the rate of return on an investment, and interest in continuous time. The text explains how to value bonds at their issue dates, at coupon times, between coupon times, and in cases where the bonds are terminated early. Next, it supplies a rapid-fire overview of the main ideas and techniques of discrete probability, including sample spaces and probability measures, random variables and distributions, expectation, conditional probability, and independence. The author introduces the basic terminology of stocks and stock trading. He also explains how to derive the rate of return on a portfolio and how to use the idea of risk aversion to model the investor tradeoff between risk and return. The text also discusses the estimation of parameters of asset models from real data. The text closes with a detailed discussion of how to value financial derivatives using anti-arbitrage assumptions. The one-step and multi-step cases are covered, and exotic options such as barrier options are also introduced, to which simulation methods are applied. Many of the examples in the book involve numerical solution of complicated non-linear equations; others ask students to produce algorithms which beg to be implemented as programs. For maximum flexibility, the author has produced the text without adhering to any particular computational platform. A digital version of this text is also available in the form of Mathematica notebooks that contain additional content.
(source: Nielsen Book Data)

• 0. ALGEBRAIC CONCEPTS. Sets. The Real Numbers. Integral Exponents. Radicals and Rational Exponents. Operations with Algebraic Expressions. Factoring. Algebraic Fractions.
• 1. LINEAR EQUATIONS AND FUNCTIONS. Solutions of Linear Equations and Inequalities in One Variable. Functions. Linear Functions. Graphs and Graphing Utilities. Solutions of Systems of Linear Equations. Applications of Functions in Business and Economics.
• 2. QUADRATIC AND OTHER SPECIAL FUNCTIONS. Quadratic Equations. Quadratic Functions: Parabolas. Business Applications Using Quadratics. Special Functions and Their Graphs. Modeling-- Fitting Curves to Data with Graphing Utilities (optional).
• 3. MATRICES. Matrices. Multiplication of Matrices. Gauss-Jordan Elimination: Solving Systems of Equations. Inverse of a Square Matrix-- Matrix Equations. Applications of Matrices: Leontief Input-Output Models.
• 4. INEQUALITIES AND LINEAR PROGRAMMING. Linear Inequalities in Two Variables. Linear Programming: Graphical Methods. The Simplex Method: Maximization. The Simplex Method: Duality and Minimization. The Simplex Method with Mixed Constraints.
• 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions and Their Properties. Equations and Applications with Exponential and Logarithmic Functions.
• 6. MATHEMATICS OF FINANCE. Simple Interest-- Sequences. Compound Interest-- Geometric Sequences. Future Values of Annuities. Present Values of Annuities. Loans and Amortization.
• 7. INTRODUCTION TO PROBABILITY. Probability-- Odds. Unions and Intersections of Events: One-Trial Experiments. Conditional Probability: The Product Rule. Probability Trees and Bayes'' Formula. Counting: Permutations and Combinations. Permutations, Combinations, and Probability. Markov Chains.
• 8. FURTHER TOPICS IN PROBABILITY-- DATA DESCRIPTION. Binomial Probability Experiments. Data Description. Discrete Probability Distributions-- The Binomial Distribution. Normal Probability Distribution. The Normal Curve Approximation to the Binomial Distribution.
• 9. DERIVATIVES. Limits. Continuous Functions-- Limits at Infinity. Rates of Change and Derivatives. Derivative Formulas. The Product Rule and the Quotient Rule. The Chain Rule and the Power Rule. Using Derivative Formulas. Higher-Order Derivatives. Applications: Marginals and Derivatives.
• 10. APPLICATIONS AND DERIVATIVES. Relative Maxima and Minima: Curve Sketching. Concavity: Points of Inflection. Optimization in Business and Economics. Applications of Maxima and Minima. Rational Functions: More Curve Sketching.
• 11. DERIVATIVES CONTINUED. Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation. Related Rates. Applications in Business and Economics.
• 12. INDEFINITE INTEGRALS. Indefinite Integrals. The Power Rule. Integrals Involving Exponential and Logarithmic Functions. Applications of the Indefinite Integral in Business and Economics. Differential Equations.
• 13. DEFINITE INTEGRALS: TECHNIQUES OF INTEGRATION. Area Under a Curve. The Definite Integral: The Fundamental Theorem of Calculus. Area Between Two Curves. Applications of Definite Integrals in Business and Economics. Using Tables of Integrals. Integration by Parts. Improper Integrals and Their Applications. Numerical Integration Methods: The Trapezoidal Rule and Simpson''s Rule.
• 14. FUNCTIONS OF TWO OR MORE VARIABLES. Functions of Two or More Variables. Partial Differentiation. Applications of Functions of Two Variables in Business and Economics. Maxima and Minima. Maxima and Minima of Functions Subject to Constraints: Lagrange Multipliers. APPENDICES. A. Graphing Calculator Guide. B. Excel Guide. C. Areas Under the Standard Normal Curve.
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MATHEMATICAL APPLICATIONS FOR THE MANAGEMENT, LIFE, AND SOCIAL SCIENCES, 12th Edition, helps students succeed in finite mathematics and applied calculus courses by tying the concepts to real-life applications using real, meaningful data. Designed for students majoring in business, economics, life sciences and social sciences, the book offers a brief review of algebra to prepare students with different backgrounds for the material in later chapters. Chapter Warm-ups review the prerequisite topics for each chapter, and Checkpoints ask questions and pose problems within each section's discussion--allowing you to check your understanding of skills and concepts before moving to the next chapter. Use of technology is integrated into the text, and optional modeling problems are discussed. Student resources include a Student Solutions Manual and online homework with WebAssign.
(source: Nielsen Book Data)

Chapters and topics have been organized in a reader-friendly manner. Ample number of solved examples and exercise problems included in each chapter. Extensive coverage of applications of mathematical modeling in business. Ideal text for all levels with real-life applications.

• Financial Mathematics: An Overview / Forward and Futures Contracts / Basic Theory of Option Pricing-I / Basic Theory of Option Pricing-II / Portfolio Optimization-I / Portfolio Optimization-II / Stochastic Processes / Ï -Fields and Conditional Expectation / Stochastic Calculus / Black-Scholes Formula Revisited / Interest Rate Modelling / Interest Rate Derivatives / Optimal Trading Strategies / Credit Risk Management / Monte Carlo Simulation/ Glossary of Financial Terms / MATLAB and Financial Toolbox / References and Index.
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"Introductory Financial Mathematics" attempts to provide an introductory text on Financial Mathematics to cater to the needs of students at various universities/ institutes in India and abroad. Apart from presenting two Nobel Prize winning theories of Black, Scholes and Merton for option pricing and Mean-Variance approach of Markowitz for portfolio optimization, the text also includes now standard topics of interest rate and interest rate derivatives. Certain interesting and useful topics e.g., Optimal Trading Strategies, Credit Scoring Models and Portfolio Credit Risk Management, which are normally not covered in a text of this kind, are also included here. A significant portion of the book is devoted to the study of Stochastics of Finance that is very much needed to understand basic concepts related to pricing of derivatives. A special care is taken to evolve a balanced approach between "precise mathematical presentation" and "economic/physical interpretations". A distinctive feature of the book is also to provide applications of MATLAB Financial Toolbox for class room teaching.
(source: Nielsen Book Data)