The remembrance of the past is the teacher of the future This paper hopes to discuss and analyze the related analysis theories in the west in the twentieth century with the stochastic theory as the main line and around the market measurement and control problems.
The first half of the 20th century is a period worthy of a great book in the history of human cultural development. All kinds of creative new theories and ideas emerge one after another. The proliferation of many new ideas makes the precipitation of nature inevitable, but it is not necessarily scum. ...
1954, Samuelson, a statistical mathematician, came across a pamphlet on speculation and investment published in 19 14 by Bacherell, which fascinated Savage very much. Therefore, he immediately sent postcards to many economists asking who had heard of Bashir. At that time, Samuelson was studying the market behavior theory and building his own evaluation model. He didn't find this book in the MIT library, but he accidentally found a doctoral thesis of Bashir. He immediately recognized the value of Bashir's works and commented that "Bashir has his own unique ideas, which are very unique", thus sharing his theory with his peers in economics. In Samuelson's early analysis of speculation, it is obvious that Bashir influenced him. At this point, the market stochastic theory, which has been lost for half a century, really entered the world's sight.
1900, Bacillier, a young French mathematician, completed a doctoral thesis entitled "Speculation" at Sorbonne University in Paris. He took the lead in using academic theories, including various mathematical tools, to explain the operation of the market with rational speculation. At the beginning of the paper, he wrote:
"Market prices reflect various events in the past, present and future at the same time, but these events usually have no obvious relationship with price changes ... human factors will also interfere, and the trading market will further respond according to its own changes. The current price fluctuation is not only a function of the previous price fluctuation, but also a function of the current state. The number of factors that determine this fluctuation is almost infinite, so it is impossible to expect to use mathematical formulas to predict ... The dynamic changes in the trading market can never become an accurate science. "
According to the foundation laid by Bashir, later mathematicians developed a complete set of probability theory, and the formula he deduced was ahead of Einstein's research on random collision of molecules in time and space. He created the concept of random process and analyzed the random changes of statistical variables, which has been widely used at present. He was also the first researcher who used theory to evaluate and study financial instruments such as futures and options. Although, his purpose is to explain why all kinds of prices in the capital market are unpredictable.
His high insight into the market comes from his careful observation of the financial market. He is convinced that, on average, there is no basis to say that the buyer or seller in the market will know the direction of the continuous movement of the market better than the other party. He then concluded: "As a collection of all speculators, at a certain point, we can't judge whether the future market price will rise or fall, and which will be more dominant, just because there are the same number of buyers and sellers in each transaction price." This makes the probability of winning or losing of speculators equal at every moment, and finally makes "the mathematical expectation of speculators equal to zero". He described this situation as "fair competition". He concluded: "At any moment, the probability of price rising and falling is equal, because the current actual price is recognized by most people. If the market has other judgments, then the quotation will not be this price. " Only when the market changes its mind for some reason and no longer recognizes the original price will the price change upward or downward. But when and how the market will change is unpredictable. So the market always has a 50% rising probability and a 50% falling probability.
Another inference of Bacherier is that if the time interval is prolonged, the fluctuation range of the market will be amplified, and an accurate conclusion has been drawn so far: "The fluctuation range is proportional to the square root of the time interval." According to Peter Bernstein's research on the fluctuation of American stock market in recent decades, a result similar to Bashir's inference is also obtained. During this period, there is a 2/3 probability that the fluctuation range of the stock price in a month, whether rising or falling, is within the range of 5.9%, and the highest fluctuation range in a year is over 72%, which is 12 times of the monthly average fluctuation range, while the annual average fluctuation range of the stock price is 20%. Here the square root of 12 is 3.46.
Bashir hopes to propose a formula to describe the possibility of market fluctuation. According to his statistical analysis, he thinks that the price fluctuation of the market in a certain period of time is difficult to predict and explain, so he focuses on the instantaneous price fluctuation of the market, hoping to establish a "probability law of price fluctuation consistent with the instantaneous price fluctuation of the market", from which he enters the field of probability theory and analyzes the spatial changes of molecules after random shocks. His most important achievement is to put forward a mathematical equation to describe this phenomenon.
Truth becomes fallacy when it takes a step forward, and Bashir's tragedy is also a historical tragedy. As Mandelbrot, the pioneer of differential geometry, said recently, no one can properly classify Bachiller's discoveries, and there is no existing tool to use his discoveries. Therefore, his research will be ignored for 60 years.
How to learn stochastic theory in financial markets? Because the stochastic theory studies the average value under the whole situation, it will be impossible to judge the situation of small samples and small probability events, because the distribution under the average state can only be established under the condition of large-scale statistics under the whole situation. Therefore, it is necessary to improve the possible position of small probability events in use, which requires strengthening the role of control in the fund management system, that is, analysts and operators can never forget the existence of unexpected situations because of historical average statistics.