The Mathematics of Financial Modeling and Investment Management (Frank J. Fabozzi Series)

the mathematics of financial modeling & investment management 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. Using Real-world Examples, This Text Introduces The Reader To The Key Mathematical Techniques Used In The Financial World, Namely Matrix Algebra, Calculus, Ordinary Differential Equations, Probability Theory, Stochastic Calculus, Time Series Analysis And Optimization. 1. From Art To Engineering In Finance -- 2. Overview Of Financial Markets, Financial Assets, And Market Participants -- 3. Milestones In Financial Modeling And Investment Management -- 4. Principles Of Calculus -- 5. Matrix Algebra -- 6. Concepts Of Probability -- 7. Optimization -- 8. Stochastic Integrals -- 9. Differential Equations And Difference Equations -- 10. Stochastic Differential Equations -- 11. Financial Econometrics: Time Series Concepts, Representations And Models -- 12. Financial Econometrics: Model Selection, Estimation, And Testing -- 13. Fat Tails, Scaling, And Stable Laws -- 14. Arbitrage Pricing: Finite-state Models -- 15. Arbitrage Pricing: Continuous-state, Continuous-time Models -- 16. Portfolio Selection Using Mean-variance Analysis -- 17. Capital Asset Pricing Model -- 18. Multifactor Models And Common Trends For Common Stocks -- 19. Equity Portfolio Management -- 20. Term Structure Modeling And Valuation Of Bonds And Bond Options -- 21. Bond Portfolio Management -- 22. Credit Risk Modeling And Credit Default Swaps -- 23. Risk Management. Sergio Focardi, Frank J. Fabozzi. Includes Bibliographical References And Index.