Online portfolio selection problems in portfolio management

Abstract

In this thesis, efforts are devoted to modeling and addressing practical problems arising in portfolio management and quantitative trading. Online portfolio selection problems with cash inflows, proportional transaction cost, and prediction method of assets’ future prices incorporating peer impact and data noise are investigated. As an application of machine learning techniques in portfolio management, online portfolio selection (OLPS) has received increasing attention in recent years. The limitation of existing online portfolio selection algorithms considering transaction costs is that the transaction remainder factor is usually derived approximately rather than precisely. This may induce an inaccurate transaction cost and suboptimal investment strategy. To tackle this problem, we introduce a novel method and solve the precise transaction remainder factor and optimal investment strategy simultaneously for each period. We also consider an open-end fund, which allows for constant cash inflows, and formulate a general framework for online portfolio selection. Based on this novel model, we design a new OLPS algorithm with transaction costs and constant cash inflows (TCI) to maximize the cumulative wealth. A framework for online portfolio selection with adaptive cash inflows is proposed. The cash inflows for each period are adjusted based on the expected returnof the next period, with the rule that greater expected returns result in larger cash inflows. Different from previous online portfolio selection studies where the future return of one single period is predicted, we try to maximize the expected return of the next two periods and derive a more farsighted portfolio strategy. The nonlinear interior point trust region optimizer algorithm is applied to approximately solve the optimization problems. Four algorithms (ACIE, ACIR, ACIE2, and ACIR2) are proposed based on the optimization results. The performance of an asset in a real financial market can be influenced by the performance of other assets in the market. 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 on the other risky assets, 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. This thesis also studied the data noise from short-lived events, trend changes in the time series data, and the dependence of multi-assets. The reversion phenomenon is exploited with multivariate robust estimates and proposes a novel online portfolio selection strategy named weighted multivariate mean reversion (WMMR). Empirical studies on various datasets show that WMMR can overcome the drawbacks of existing mean reversion algorithms and outperform existing results.