The Mathematics of Financial Modeling and Investment Management
Since the pioneering work of Harry Markowitz in the 1950s, sophisticated statistical and mathematical techniques have increasingly made their way into finance and investment management. One might question whether all this mathematics is justified, given the present state of economics as a science. However, a number of laws of economics and finance theory with a bearing on investment management can be considered empirically well established and scientifically sound. This knowledge can be expressed only in the language of statistics and mathematics. As a result, practitioners must now be familiar with a vast body of statistical and mathematical techniques.
Different areas of finance call for different mathematics. Investment management is primarily concerned with understanding hard facts about financial processes. Ultimately the performance of investment management is linked to an understanding of risk and return. This implies the ability to extract information from time series that are highly noisy and appear nearly random. Mathematical models must be simple, but with a deep economic meaning.
In other areas, the complexity of instruments is the key driver behind the growing use of sophisticated mathematics in finance. There is the need to understand how relatively simple assumptions on the probabilistic behavior of basic quantities translate into the potentially very complex probabilistic behavior of financial products. Derivatives are the typical example.
This book is designed to be a working tool for the investment management practitioner, student, and researcher. We cover the process of financial decision-making and its economic foundations. We present financial models and theories, including CAPM, APT, factor models, models of the term structure of interest rates, and optimization methodologies. Special emphasis is put on the new mathematical tools that allow a deeper understanding of financial econometrics and financial
economics. For example, tools for estimating and representing the tails of the distributions, the analysis of correlation phenomena, and dimensionality reduction through factor analysis and cointegration are recent advances in financial economics that we discuss in depth.
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