Construction and analysis of continuous maximum entropy stock price prediction model—Based on the utility function including transaction costs

Abstract

Random-walk theory suggests that stock prices are random fluctuations over time, so the stock price is a random variable over time. Base on the theory of Brownian motion, the random-walk theory, and the maximum entropy principle. We can build a forecasting model of the continuous maximum entropy stock price. The objective function is a maximum entropy function. In the maximum entropy function, the stock price as a continuous random variable. Because in this paper we make the present value of the stock at time t as the consumer's utility function, so we can make a prior condition as the constraint conditions. The utility function will be content the prior condition. In order to make it easily for us to obtain the probability distribution, we can make the stock price as the random variable into a new random variable of contains the logarithm. So the model is transformed into a new model, named continuous maximum entropy stock price forecasting model. Because the optimization problem is convex programming, so we can construct the Lagrange function to solve the continuous maximum entropy stock price forecasting model. To the end, when the density function submits to the normal distribution, the entropy function will be the maximum. So we can deduce the expected value of the stock price in the future. As in the real stock trading will generate some action costs, the paper adds he transaction costs into the utility function, there will be make the model more realistic, which can more accurately predict future stock market stock prices.