First, financial mathematics is a new discipline and an important part of "financial high technology". The research goal is to make use of some advantages in China's mathematics field, deeply analyze the mathematical theory of financial market equilibrium and securities pricing, establish a mathematical model suitable for China's national conditions, write certain computer software, simulate theoretical research results, conduct econometric analysis and research on actual data, and provide in-depth technical analysis and consultation for the actual financial sector. The core content is to study the optimal selection theory of portfolio and the asset pricing theory under uncertain random environment. Arbitrage, optimality and equilibrium are the basic ideas of economics and the three basic concepts of financial mathematics.

Two, the main research contents of financial mathematics and the problems to be solved mainly include:

(1) securities and portfolio pricing theory

Develop the pricing theory of securities (especially derivatives such as futures and options). The mathematical method used is mainly to put forward a suitable stochastic differential equation or stochastic difference equation model to form the corresponding backward equation. The corresponding nonlinear Feynman-Kac formula is established, and a very general extended Black-Scholes pricing formula is derived from it. The backward equation will be a high-dimensional nonlinear singular equation with constraints.

This paper studies the pricing of portfolio with different maturities and yields. It is necessary to establish a mathematical model combining pricing and optimization. In the study of mathematical tools, it may be necessary to study stochastic programming, fuzzy programming and optimization algorithms.

Under the condition of incomplete market, the pricing theory related to preference is introduced.

(2) Incomplete market economy equilibrium theory (GEI)

It is planned to conduct research in the following aspects:

1. Infinite dimensional space, infinite horizontal space and infinite state.

2. Stochastic economy, no arbitrage equilibrium, change of economic structure parameters, nonlinear asset structure.

3. Innovation and design of asset securitization.

4. Friction economy

5. Corporate Behavior and Production, Bankruptcy and Bad Debt

6. Securities market game.

(3) The application of GEI's plate equilibrium algorithm and Monte Carlo method in the calculation of economic equilibrium point, the application of GEI theory in macro-control of finance, finance and economy, and the study of natural resource asset pricing and sustainable utilization under the framework of the theory of sustainable development under incomplete market conditions.