"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 co integration 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.