The Mathematics of Financial Modeling & Investment Management covers a wide range of technical topics in mathematics and finance-enabling the investment management practitioner, researcher, or student to fully understand the process of financial decision-making and its economic foundations. This comprehensive resource will introduce you to key mathematical techniques-matrix algebra, calculus, ordinary differential equations, probability theory, stochastic calculus, time series analysis, optimization-as well as show you how these techniques are successfully implemented in the world of modern finance. Special emphasis is placed on the new mathematical tools that allow a deeper understanding of financial econometrics and financial economics. Recent advances in financial econometrics, such as tools for estimating and representing the tails of the distributions, the analysis of correlation phenomena, and dimensionality reduction through factor analysis and cointegration are discussed in depth. Using a wealth of real-world examples, Focardi and Fabozzi simultaneously show both the mathematical techniques and the areas in finance where these techniques are applied. They also cover a variety of useful financial applications, such as: * Arbitrage pricing * Interest rate modeling * Derivative pricing * Credit risk modeling * Equity and bond portfolio management * Risk management * And much more Filled with in-depth insight and expert advice, The Mathematics of Financial Modeling & Investment Management clearly ties together financial theory and mathematical techniques.Preface. Acknowledgments. About the Authors. Commonly Used Symbols. Abbreviations and Acronyms. Chapter 1. From Art to Engineering in Finance. Chapter 2. Overview of Financial Markets, Financial Assets, and Market Participants. Chapter 3. Milestones in Financial Modeling and Investment Management. Chapter 4. Principles of Calculus. Chapter 5. Matrix Algebra. Chapter 6. Concepts of Probability. Chapter 7. Optimization. Chapter 8. Stochastic Integrals. Chapter 9. Differential Equations and Difference Equations. Chapter 10. Stochastic Differential Equations. Chapter 11. Financial Econometrics: Time Series. Chapter 12. Financial Econometrics: Model Selection, Estimation, and Testing. Chapter 13. Fat Trails, Scaling, and Stable Laws. Chapter 14. Arbitrage Pricing: Finite-State Models. Chapter 15. Arbitrage Pricing: Continuous-State, Continuous-Time Models. Chapter 16. Portfolio Selection using Mean-Variance Analysis. Chapter 17. Capital Asset pricing Model. Chapter 18. Multifactor Models and Common Trends for Common Stocks. Chapter 19. Equity Portfolio Management. Chapter 20. Term Structure Modeling and Valuation of Bonds and Bond Optics. Chapter 21. Bond Portfolio Management. Chapter 22. Credit Risk Modeling and Credit Default Swaps. Chapter 23. Risk Management.
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