Robust online portfolio optimization with cash flows

One fundamental issue in finance is portfolio selection, which seeks the best strategy for assigning capital among a group of assets. There has been growing interest in online portfolio selection where the investment strategy is frequently readjusted in a short time as new financial market data arrives constantly. Numerous effective algorithms have been extensively examined both in terms of theoretical analysis and empirical evaluation. Previous online portfolio selection algorithms that incorporate transaction costs are limited by the fact that they often approximate the transaction remainder factor instead of calculating it precisely. This could lead to suboptimal investment performance. To address this issue, we present an innovative method that considers transaction costs and resolves the accurate transaction remainder factor and the optimal portfolio allocation simultaneously for each period. In addition, we take into account the open-end fund, which permits constant cash inflows, and develop a framework for online portfolio selection. We also incorporate the uncertainty set to minimize the impact of the prediction error during the prediction process. Utilizing the framework presented in this innovative model, we develop a novel algorithm for online portfolio selection that incorporates transaction costs and continuous cash inflows with the objective of maximizing cumulative wealth. Numerical experiments show that the proposed algorithms are able to handle transaction costs and constant cash inflows effectively.