Financial mathematics is a subject that studies financial markets, financial product pricing, risk management and other issues, and its application direction is very wide. The following are some major application areas:

1. financial engineering: financial engineers use financial mathematical tools and methods to design and develop new financial products and strategies, such as derivative pricing and risk management.

2. Investment management: Investment managers use financial mathematical models to predict the price trends of stocks, bonds and other investment products in order to formulate investment strategies.

3. Risk management: Financial institutions use financial mathematical models to evaluate and manage various risks, such as credit risk, market risk and operational risk.

4. Asset management: Asset management companies use financial mathematical models to optimize their portfolios to maximize returns or minimize risks.

5. Insurance industry: Insurance companies use financial mathematical models to evaluate and manage insurance risks, such as premium pricing and payout ratio forecasting.

6. Credit score: Financial institutions use financial mathematical models to evaluate the credit risk of borrowers, so as to decide whether to provide loans and the interest rate and duration of loans.

7. Quantitative trading: quantitative traders use financial mathematical models to formulate trading strategies and make profits through a large number of fast transactions.

8. Behavioral finance: Behavioral financiers use financial mathematical models to study investors' behaviors and decision-making processes to explain abnormal phenomena in financial markets.

9. Macroeconomic analysis: Economists use financial mathematical models to analyze and predict economic trends, such as economic growth, inflation and unemployment rate.