In the 21st century, mathematical technology, like computer technology, has become an essential tool in the development of any science. Collins, vice president of Citigroup

Bank in the United States, stated in his speech

at Newton Institute of Mathematical Sciences, Cambridge University, England on March 6, 1995: "At the beginning of the 18th century, Bernoulli, a famous mathematician of Newton's contemporaries, declared:' People who study physics

but don't understand mathematics actually deal with things of little significance.' At that time, this statement was

true for physics, but not necessarily true for banking. In the 18th century, you could run a bank without any math training. What used to be true for physics is also true for banking now. So now we can

say:' People who work in banking but don't know mathematics actually deal with things that are of little significance'. He also

pointed out that 7% of Citibank's business depends on mathematics, and he particularly emphasized that' without the tools and technology developed by mathematics, we can't do anything about many things ... without mathematics, we can't survive. Here the bank

describes the importance of mathematics with his experience. After the end of the Cold War, thousands of scientists who used to work in the military system in the United States entered Wall Street, and large-scale fund management companies began to hire doctors in mathematics or physics. This is an important signal: the financial market is not a battlefield, but it is far better than the battlefield. However, both the market and the battlefield are inseparable from the complicated and rapid calculation work.

However, in China, we can't avoid the fact that professionals with higher education can read domestic core journals of economics and finance, but it is difficult for undergraduates majoring in domestic finance to read the international core journal Jo

Journal of Finance. Few managers of securities investment funds read Joural of Portfolio Management

ment, the reason lies not in the proficiency of foreign languages, but in the differences in content and research methods. At present, compared with

, most domestic managers focus on describing the definition of finance, market division and financial organization, or describing finance. On the other hand, foreign academic and practical circles mainly focus on quantitative analysis, such as the principle of capital asset pricing, the replication method of derivative assets, etc., or it is called analytical finance. Even in the textbooks of domestic finance, although the pricing of Underlying asset and derivative assets is involved, the original proof of the formula is avoided. This phenomenon is unreasonable, and the reasons for this phenomenon are as follows: firstly, according to the different research methods, China's financial disciplines can be attributed to the Planning Office of Philosophy and Social Sciences in China or to the Management Science Department of the National Natural Science Foundation of China, with the former playing a major role and most of this team coming from philosophy and political science before the economic transition, so the research methods are mostly qualitative. In the west, on the contrary, the team in the financial < P > research direction has a good foundation in mathematics and physics. Secondly, it is determined by the actual environment of China's financial market. China's

securities market has just started, and there is no unified money market. Investors are mainly composed of small and medium-sized investors, and the market

has a high speculative component, so there will be no demand for modern investment theory. Correspondingly, it is difficult for academic circles to generate enthusiasm for

research.

However, with its precise description and strict deduction, mathematical technology has indisputably entered the financial field. Since Markowitz put forward in 1952

qualitative and liquidity, it has been difficult to distinguish whether a world-class financial magazine is analyzing the financial market or writing a

mathematical paper. Going back to Collins' speech, in the trend of financial securitization, no matter whether we use statistical methods to analyze historical data, look for the law of price fluctuation, or use mathematical analysis methods to copy financial products, whoever discovers the internal law first will get high profits in the ever-changing financial market. Although the entry of mathematics into the financial field has been rejected and ignored due to the strict entry into the fortress, in order to pursue profits, the fear of the unknown is vulnerable.

So, in the future, we can imagine such an industrial chain full of bright prospects: financial market-financial mathematics-

computer technology. There are huge profits and high risks in the financial market, which need the help of computer technology to analyze. However, it is impossible to calculate < P > with descriptive language such as approximate, left and right, and it can only identify the space composed of and 1 in essence. Financial mathematics just plays an intermediary role in the process of < P >, and it can describe the randomly fluctuating market with accurate language. For example,

found the risk-free discount factor without arbitrage through the rate of return state matrix. Therefore, Financial Mathematics can help

IT industry to extend to the financial industry and gain its own profit space

Financial mathematics, also known as mathematical finance, mathematical finance and analytical finance, uses mathematical tools to study finance, and makes quantitative analysis such as mathematical modeling, theoretical analysis and numerical calculation, in order to find the inherent 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 very active preface disciplines at present.

financial mathematics is a new discipline and an important part of "financial high technology". It is of great significance to study financial mathematics. The general research goal of financial mathematics is to make use of the advantages of some aspects 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 the theoretical research results, conduct econometric analysis and research on the actual data, and provide in-depth technical analysis and consultation for the actual financial sector.

The main research contents and problems to be solved in financial mathematics include:

(1) Pricing theory of securities and portfolio

Developing 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, from which the very general extended Black-Scho1es pricing formula is derived. The backward equation obtained will be a high-dimensional nonlinear singular equation with constraints.

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

under the condition that the market is incomplete, the pricing theory related to preference is introduced.

(2) incomplete market economy equilibrium theory (GEI)

It is planned to study the following aspects:

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

2. Stochastic economy, arbitrage-free equilibrium, economic structural parameter Friction, non-linear asset structure

3. Innovation of asset securities and

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

At present, Peking University, Fudan University, Zhejiang University, Shandong University and Nankai University are among the universities offering undergraduate courses in financial mathematics in China.

Later, I was very good at computer work. Financial mathematics will later engage in research and analysis in the fields of banking, insurance, stocks and futures, or do software development in these fields, with a good professional background, and these fields will be very important in the future.

There are few financial mathematicians in China

The Nobel Prize in Economics has been awarded to economists who use mathematics as a tool to analyze financial problems at least three times. Professor Wang Duo from the Department of Financial Mathematics in Peking University said, but unfortunately, the training of relevant talents in China has just started. Nowadays, compound talents who know both finance and mathematics are quite scarce.

financial mathematics, a new interdisciplinary subject, has become a wonderful flower in the international financial community. The 23 Nobel Prize in Economics just announced is to commend American economist Robert Engel and British economist clive granger for their two new methods of analyzing economic time series, namely "variability with time" and "* * * same trend", which have brought great influence on economic research and economic development.

Wang Duo said that the development of financial mathematics has twice triggered the "Wall Street Revolution". In the early 195s, Markowitz put forward the portfolio theory of securities, and for the first time, he clearly gave the investment method with the greatest possible return by investing in various securities in different proportions at a certain risk level with mathematical tools, which triggered the first "Wall Street Revolution". In 1973, Blake and Scholes gave the option pricing formula by mathematical method, which promoted the development of option trading, and option trading soon became the main content of the world financial market and became the second "Wall Street Revolution".

Today, financial mathematicians have become one of the most sought-after talents on Wall Street. The simplest example is that the highest status and income among insurance companies may be the chief actuary. Paul Coslin, vice chairman of Citibank in the United States, famously said, "A person who is engaged in banking business and doesn't know mathematics can only do trivial things."

In the United States, famous universities such as the University of Chicago, the University of California, Berkeley, Stanford University, Carnegie Mellon University and new york University have all established degrees or professional certificate education related to financial mathematics.

Experts believe that the possible development of financial mathematics should be highlighted in Asia, especially in China, where the financial market is being developed and has great potential. The Chinese University of Hong Kong, University of Science and Technology, City University of Technology and other schools have launched relevant training courses and training plans, which have received enthusiastic response from the banking and financial industry. However, the training of this talent in China Mainland is somewhat difficult.

Wang Duo introduced that the National Natural Science Foundation of China included the research content of financial engineering in a major project in the Ninth Five-Year Plan, which can be said to have launched the domestic financial mathematics research in an all-round way. But this is nearly half a century later than Markowitz's research and application of financial mathematics.

under the background that financial derivatives have become an important role in the international financial market, China's financial derivatives have just started, and financial derivative instrument is almost blank. "After joining W TO, international financiers will definitely bring this series of businesses to China. If there are no corresponding products and talents, how can we compete? " Wang Duo said anxiously.

He believes that in recent years, the Mexican financial crisis and the collapse of the century-old Bahrain Bank have warned us that if we do not master modern financial technologies such as financial mathematics, financial engineering and financial management, and lack talents, we may suffer great losses in international financial competition. What we lack most now is senior compound talents who can master modern financial derivatives and make quantitative analysis of financial risks, and who know both finance and mathematics.

It is reported that many colleges and universities in China have started teaching related to financial mathematics, but the graduates are far from meeting the needs of the whole market.

Wang Duo believes that there are still some insurmountable obstacles in cultivating such talents-financial mathematics will eventually be applied to practice, but at present, there is no climate in financial derivative instrument, so it is difficult for students to have the opportunity to practice, and teaching and learning are still on paper. In addition, most of the people trained in colleges and universities are undergraduates, only a small number of graduate students, and high-end talents in this field are still rare in China. The state should pay more attention to the cultivation of compound talents combining finance and mathematics.

Wang Duo recalled that in 1997, when Peking University established the first financial mathematics department in China, he wanted to run a school with some financial people. But quite a few people are obviously not interested in this: "What financial derivatives and financial mathematics are all things that the country should worry about."

Although some people thought that the Department of Financial Mathematics was too advanced when it was first opened, Wang Duo insisted that education should be ahead of industrial development in order to reserve talents for the market. If we don't pay attention to the training of talents in related fields today, it may lead to our disadvantage in international competition.

The reporter found that even today, on this issue, on the one hand, teachers in colleges and universities are worried about the scarcity of talents, on the other hand, some famous experts are indifferent to the cultivation of financial mathematics talents.

during the interview, the reporter tried to contact several experts in domestic financial mathematics or financial theory many times, but they were repeatedly rejected. The reason is very simple. They think that talking about talent training is too childish, and some even say, "I don't understand and don't care about talent training at all." Others said, "I have a lot of topics to do now, which is more important, my topic or discussing personnel training", "I don't have the time and obligation to explain the Nobel Prize in Economics to the public, and it has nothing to do with me whether the people know financial mathematics".

[ Edit this paragraph] Data mining in finance

1. What are association rules

Before describing some details about association rules, let's look at an interesting story: diapers and beer.

In a supermarket, there is an interesting phenomenon: diapers and beer are sold together. But this strange move has increased the sales of diapers and beer. This is not a joke, but a real case that happened in the supermarket chain of Wal-Mart in the United States, and it has always been talked about by merchants. Wal-Mart has the largest data warehouse system in the world. In order to accurately understand customers' buying habits in its stores, Wal-Mart conducts a shopping basket analysis of its customers' shopping behavior and wants to know what products customers often buy together. Wal-Mart's data warehouse concentrates on the detailed original transaction data of its stores. On the basis of these original transaction data, Wall