A Maximum Entropy Model for Large-Scale Portfolio Optimization

Based on the maximum entropy theory, this paper presents a new model for solving the large scale portfolio problem. Unlike Markowitzpsilas model, this new model is not based upon any probabilistic assumption on the distribution of stock data in the market, so it is more suitable for the solution of real problem. By some simplification, we derive a convex program model. It is with separable variables and the dual program is unconstrained and explicit. The number of dual variables is equal to that of the moment constraints in the primal problem. Therefore it is suitable to solve the large scale portfolio optimization problem which has a little information, such as the mean and variance of the rates of return. Using one sample data, we calculate the optimal portfolio with our model and Markowitz's. From the results we can see that ours is better at the same level of the desired mean or accepted variance.