Financial mathematics, also known as analytical finance, mathematical finance and mathematical finance, is an interdisciplinary subject of mathematics and finance that rose in the late 1980s and early 1990s. Financial mathematics mainly uses modern mathematical theories and methods (such as stochastic analysis, stochastic optimal control, combinatorial analysis, nonlinear analysis, multivariate statistical analysis, mathematical programming, modern calculation methods, etc.). ) the theory and practice of quantitative analysis and research on finance (including investment, bonds, funds, stocks, futures, options and other financial instruments and markets). ). Its core issues are the selection theory of optimal investment strategy and the asset pricing theory under uncertain conditions. Arbitrage, optimality and equilibrium are three main concepts. In recent twenty years, financial mathematics has not only had a direct impact on the innovation of financial instruments and the effective operation of financial markets, but also been widely used in the investment decision-making of companies, the evaluation of R&D projects (such as real options) and the risk management of financial institutions.

In modern financial mathematics theory, various financial and economic models occupy a central position. There are still remarkable achievements: efficient market theory, portfolio theory, capital asset pricing model, arbitrage pricing theory, option pricing equation and asset structure theory.