Financial mathematics, also known as mathematical finance, mathematical finance and analytical finance, uses mathematical tools to study finance, carries out quantitative analysis such as mathematical modeling, theoretical analysis and numerical calculation, so as to discover the internal laws of finance and guide practice. Financial mathematics can also be understood as the application of modern mathematics and computing technology in the financial field. Therefore, financial mathematics is a new interdisciplinary subject, which develops rapidly and is one of the most active frontier disciplines at present.

Actuarial science has a history of 300 years in the west. It is a subject that uses mathematical theories such as probability theory and various financial tools to study the quantitative methods and techniques of how the insurance industry and other financial industries deal with various risks. It is the theoretical basis for the development of modern insurance, financial investment and social security.

Actuarial science is a science that uses the theory of probability mathematics and various financial tools to analyze and predict economic activities. In western developed countries, actuarial science plays an important role in insurance, investment, financial supervision, social security and other fields related to risk management. Actuaries deal with "future uncertainty", and their purpose is to provide basis for financial decision-making.