Financial Mathematics is a field of applied mathematics, which identifies problems in Finance and provides elegant solutions using methods from probability theory, partial differential equations, optimization and numerical methods.

In Financial Mathematics, the main emphasis is given to the derivation of the mathematical models that confirm the intuition from Financial Economics. For example, the seminal case of the Black-Scholes-Merton model, and its many extensions such as stochastic volatility, pure jump processes and collateral funding, is built around the No-Arbitrage assumption and assumes as given the evolution of the stock price in order to find the prices of derivative securities.