This major trains students to master the basic theories and ways of thinking of financial mathematics and economic finance, and basically master the application of modern mathematics and architectural science in economic development, business information prediction and analysis, management decision-making, and deal with practical financial problems such as enterprise financial accounting, portfolio analysis, project investment evaluation, insurance actuarial, etc. , with strong mathematical modeling ability and basic science and technology development ability.
Professional introduction
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, portfolio 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.
The major of financial mathematics pays attention to the cultivation of modern financial theory, mathematical foundation and computer application ability, the combination of theory and practice, the cultivation of students' practical ability, and the correct guidance of financial literacy such as professional ethics and attitude. Relying on the advantages of comprehensive development of economics, law, management, literature and other disciplines, this major highlights the characteristics of cross-integration of finance and mathematics. Based on economics, with mathematics and computers as tools and finance as the core, it focuses on cultivating students' financial quantitative analysis and application ability, and cultivating students to master modern financial mathematics theory, be familiar with financial operations, and especially have strong financial quantitative analysis and application ability. This major has established a fixed professional practice base with many financial institutions and enterprises such as banks, insurance companies, securities investment companies, etc., which has provided good practical teaching and practice training conditions for students of this major.
Talent situation
Domestic universities offering undergraduate courses in financial mathematics include Peking University, Fudan University, Shandong University of Finance and Economics, Shandong University, Zhejiang University, Nankai University and Southwestern University of Finance and Economics. In particular, Shandong University, Shandong University of Finance and Economics and Fudan University are in the leading position in financial mathematics research in the world. There are few financial mathematicians in China, and the Nobel Prize in Economics has been awarded at least three times to economists who use mathematics as a tool to analyze financial problems. Professor Wang Duo from the Department of Financial Mathematics in Peking University said, "Mathematics will definitely make great contributions to finance" and "Modern finance cannot be separated from mathematics". But unfortunately, the training of relevant talents in China has just started. Nowadays, compound talents who know both finance and mathematics are quite scarce.
Development history
The history of financial mathematics can be traced back to 1900 Bachellier's doctoral thesis "Speculation", which announced the birth of financial mathematics. In this paper, he used Brownian motion to describe the change of stock price for the first time. He believes that in the capital market, there are buyers and sellers, the buyer is bullish and the seller is bearish. Price fluctuation is Brownian motion, and its statistical distribution is normal distribution. However, Bachiller's work has not attracted the attention of financial circles for more than 50 years. In the early 1950s, Samuelson rediscovered Bacceli's work through the statistician Savage, which marked the beginning of modern finance. Modern finance then experienced two great revolutions, the first in 1952. That year, 25-year-old Markowitz published his doctoral thesis and put forward the mean variance theory of portfolio selection. Its significance lies in guiding the original idea that people expect to find the "best" stock to the understanding of the quantification and balance of risks and benefits. The main idea of the above-mentioned mean variance theory is to maximize the expected return at a given risk level, or to minimize the risk at a given income level. Later, Sharp and lintner further expanded markowitz's work and put forward CAPM. Later, Miller's corporate finance theory (MM theory) triggered the first "Wall Street Revolution", which was the beginning of financial mathematics. Markowitz and Sharp also won the 1990 Nobel Prize in Economics for their pioneering contributions in financial mathematics.
The main research contents and problems to be solved in financial mathematics 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.
Training objectives
Based on the characteristics and resources of running a school, this major establishes a perfect and feasible whole-process application-oriented financial teaching mode, and cultivates application-oriented financial talents with good scientific and cultural literacy, which can effectively transform knowledge into ability, innovative and practical ability and personalized differences. The expectation of this major for students five years after graduation: one year to be familiar with the working environment, two years to consolidate professional ability, three years to improve work quality, four years to innovate work ability and five years to enhance their own value.
Ideological, political and moral qualities. Have good ideological and political literacy and moral literacy, practice socialist core values, have humanities and social sciences literacy and a high sense of social responsibility.
Basic knowledge and skills. Master the basic theories and methods of financial mathematics, be able to design and develop new financial tools, and skillfully use computers to analyze financial data.
Comprehensive ability and innovative practice. Have the ability to handle the basic business of financial institutions and solve practical financial problems, and comprehensively use various financial tools and quantitative analysis methods to solve practical financial problems. Have a firm professional ideal and professional identity, and be competent in banking, insurance, securities and other financial departments or related economic departments.