Study On Fluctuations Of Stock Prices By Stochastic Model And Grey System

In the stock market, stock prices directly reflect the market conditions. The study on stock price process is one of the most important part in the mathematical finance. In this paper, we apply the voter model which is one of the statistical physics model and grey model to study on the fluctuations of stock prices. The paper contains two parts.In part one, because of the instability of the financial phenomenon, the stochastic processes theory which is an important part of probability is applied to do a research of the financial problems. Applying the Voter model and the theory of stopping time, we construct the return process of a stock in a stock market. From this return process, we can derive the corresponding stock price process. We show that the probability distributions of the stock price converge to the corresponding distribution of the Black-Scholes model. This implies that the financial model of the present paper is somewhat useful for us to understand the statistical properties of the fluctuations for the stock prices.In part two, because of the influence of the political, economic, market and the enterprises themselves, the fluctuations of stock prices is unsystematic and frequent. There is a certain limitations in the analysis and forecasting of the stock price, and the result is no very well too. So, we believe that the stock market is a system that we only know part of information, there is still something we don't know. We consider the stock market as a grey system, and the stock price is the gray volume of this system. In this paper, we apply the grey system to forecast the stock price. We did some improvements in the residual model of grey model to improve the accuracy of GM (1,1). Through the empirical analysis, we proved it.