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Mathematical finance is an applied mathematics field that works with actual financial situations to determine pricing models and resource values. It is the opposite end of the theoretical study of financial economics. In practice, a financial economist will study a phenomenon and come up with theoretical examples of how it would apply to the real world. A person in the mathematical finance field would take that theory and apply it to real-world situations in order to derive value or gain information that will generate profit.
The study of mathematical finance began in the early 1900s, but the field didn’t really take off until many years later. Early uses of mathematical finance helped generate stock portfolios, a practice that is still used today. In the later part of the 20th century, people began using the science as a means of modeling entire markets. This practice culminated in the drastic economic downturn of the early 21st century and a significant black eye for the science.
The science of mathematical finance studies economic theory as it applies to real world economics. This applies to all forms of economics, from a single company’s stock price all the way to a full economic market. Since the theoretical field of financial economics continues to generate theories across the field, mathematical finance continues to find new avenues of application.
On a small scale, this science is well-suited for putting together stock portfolios. Using a basic mathematical model, it is possible to collect a group of stock that has a very high gain-to-loss ratio. This means that while some stocks may lose and some may stagnate, the whole portfolio makes money.
Before mathematical finance, the excepted method of putting together a portfolio was simple to find high-yield stocks. This practice had a major drawback—while it provided income, it didn’t support smaller companies. Since smaller companies carry a lot of innovation, their stock prices are the most likely to make fast and significant gains. Before the models involved in mathematical finance, these gains were often outside the reach of more conservative investors.
On a large scale, this science attempts to simulate entire markets. The models created by mathematical finance draw on a wide range of different sciences. For instance, if a person were mapping growth in an agricultural market, they would need to gather historical and meteorological data as well as the financial information on the market. All of these disparate sciences come together to create a simulation of the market as a whole. Based on the results of the created model, investors can plan their individual strategies.