Online Portfolio Selection Strategy Based on Combining Experts' Advice

The weak aggregating algorithm (WAA) developed from learning and prediction with expert advice makes decisions by considering all the experts' advice, and each expert's weight is updated according to his performance in previous periods. In this paper, we apply the WAA to the online portfolio selection problem. We first consider a simple case in which the expert advice is the strategy for investing in one stock; for this case, we obtain a portfolio selection strategy WAAS and prove that the WAAS can identify the best stock. We also discuss a more complicated case in which constant rebalanced portfolios are considered as expert advice, and obtain a corresponding portfolio selection strategy WAAC. The theoretical result shows that the cumulative gain that WAAC achieves is as large as that of the best constant rebalanced portfolio. Numerical analysis shows that the cumulative gains of our proposed strategies are as large as those of the best expert advice.