Mathematical finance is the branch of applied mathematics concerned with the financial markets .
The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive, and extend, the mathematical or numericalmodels suggested by financial economics. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the fair value of derivatives of the stock .
In terms of practice, mathematical finance also overlaps heavily with the fields of financial engineering and computational finance . Arguably, all three are largely synonymous, although the latter two focus on application, while the former focuses on modelling and derivation; see Quantitative analyst .
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Mathematical tools
Derivatives pricing
Source: Wikipedia