Financial Mathematics is the field of applied mathematics that involves defining problems in finance and providing solutions using methods that draw from probability, statistics, differential equations, optimization, numericalmethods, and data science.
The primary emphasis in financial mathematics is 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.
The unifying premise for financial mathematics is more than just a collection of techniques applied to a common problem area. Rather, it quantifies and enables much of the modern interplay in global markets among companies, investors, and financial agents, often constrained or constructed by the actions of central banks, regulators and governments. Global financial institutions develop and provide products and services that are vital to the course of capital allocation, investment, and risk transfer. None of this could occur without the sophisticated approaches enabled by financial mathematics which have evolved over the past 25 years.
