Mathematical Finance

 

Mathematical finance comprises the branches of applied mathematics concerned with the financial markets.
 Mathematical finance is closely associated with the discipline of financial economics mathematical finance will derive, and expand, the mathematical or numerical models recommended by financial economics. For example, a financial economist studies the structural reasons why a company has a certain share price, a financial mathematician takes the share price as a given, and try to use stochastic calculus to obtain the fair value of derivatives of the stock.
Practically, Mathematical finance overlaps greatly with the field of computational finance also famously known as financial engineering. The latter focuses on application, while the former focuses on modeling and derivation.
Many universities around the world now offer degree and research programs in mathematical finance.
The history of mathematical finance starts with The Theory of Speculation The first influential work of mathematical finance is the theory of portfolio optimization by Harry Markowitz on using mean-variance estimates of portfolios to judge investment strategies,
With time, the mathematics has become more sophisticated. Thanks to Robert Merton and Paul Samuelson, one-period models were replaced by continuous time.
The next foremost revolution in mathematical finance came with the work of Fischer Black and Myron Scholes along with fundamental contributions by Robert C. Merton, by modeling financial markets with stochastic models.