Adaptive online mean-variance portfolio selection with transaction costs

Online portfolio selection is attracting increasing attention in both artificial intelligence and finance communities due to its efficiency and practicability in deriving optimal investment strategies in real investment activities where the market information is constantly renewed every second. The key issues in online portfolio selection include predicting the future returns of risky assets accurately given historical data and providing optimal investment strategies for investors in a short time. In the existing online portfolio selection studies, the historical return data of one risky asset is used to estimate its future return. In this paper, we incorporate the peer impact into the return prediction where the predicted return of one risky asset not only depends on its past return data but also the other risky assets in the financial market, which gives a more accurate prediction. An adaptive moving average method with peer impact (AOLPI) is proposed, in which the decaying factors can be adjusted automatically in the investment process. In addition, the adaptive mean-variance (AMV) model is firstly applied in online portfolio selection where the variance is employed to measure the investment risk and the covariance matrix can be linearly updated in the investment process. The adaptive online moving average mean-variance (AOLPIMV) algorithm is designed to provide flexible investment strategies for investors with different risk preferences. Finally, numerical experiments are presented to validate the effectiveness and advantages of AOLPIMV.