Preface

Since the pioneering work of Harry Markowitz in the 1950s, mathematical tools drawing from the fields of standard and stochastic calculus, set theory, probability theory, stochastic processes, matrix algebra, optimization theory, and differential equations have increasingly made their way into finance. Some of these tools have been used in the development of financial theory, such as asset pricing theory and option pricing theory, as well as like theories in the practice of asset management, risk management, and financial modeling.

Different areas of finance call for different mathematics. For example, asset management, also referred to as investment management and money management, is primarily concerned with understanding hard facts about financial processes. Ultimately, the performance of an asset manager is linked to an understanding of risk and return. This implies the ability to extract information from time series data 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. Examples of such products include option-type financial derivatives (such as options, swaptions, caps, ...

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