We propose a set of novel radial basis functions with adaptive input and composite trend representation (AICTR) for portfolio selection (PS). Trend representation of asset price is one of the main information to be exploited in PS. However, most state-of-the-art trend representation-based systems exploit only one kind of trend information and lack effective mechanisms to construct a composite trend representation. The proposed system exploits a set of RBFs with multiple trend representations, which improves the effectiveness and robustness in price prediction. Moreover, the input of the RBFs automatically switches to the best trend representation according to the recent investing performance of different price predictions. We also propose a novel objective to combine these RBFs and select the portfolio. Extensive experiments on six benchmark data sets (including a new challenging data set that we propose) from different real-world stock markets indicate that the proposed RBFs effectively combine different trend representations and AICTR achieves state-of-the-art investing performance and risk control. Besides, AICTR withstands the reasonable transaction costs and runs fast; hence, it is applicable to real-world financial environments.

Portfolio optimization can be roughly categorized as the mean-variance approach and the exponential growth rate approach based on different theoretical foundations, trading logics, optimization objectives, and methodologies. The former and the latter are often used in long-term and short-term portfolio optimizations, respectively. Although the mean-variance approach could be applied to short-term portfolio optimization, the performance may not be satisfactory (same with the exponential growth rate approach to the long-term portfolio optimization). This survey mainly explores the gaps between these two approaches, and investigates what common ideas or mechanisms are beneficial. Besides, the evaluating framework of this field and some unsolved problems are also discussed.

In this paper, we propose a novel reweighted price relative tracking (RPRT) system for automatic portfolio optimization (APO). In the price prediction stage, it automatically assigns separate weights to the price relative predictions according to each asset's performance, and these weights will also be automatically updated. In the portfolio optimizing stage, a novel tracking system with a generalized increasing factor is proposed to maximize the future wealth of next period. Besides, an efficient algorithm is designed to solve the portfolio optimization objective, which is applicable to large-scale and time-limited situations. Extensive experiments on six benchmark datasets from real financial markets with diverse assets and different time spans are conducted. RPRT outperforms other state-of-the-art systems in cumulative wealth, mean excess return, annual percentage yield, and some typical risk metrics. Moreover, it can withstand considerable transaction costs and runs fast. It indicates that RPRT is an effective and efficient APO system.

We propose a novel linear learning system based on the peak price tracking (PPT) strategy for portfolio selection (PS). Recently, the topic of tracking control attracts intensive attention and some novel models are proposed based on backstepping methods, such that the system output tracks a desired trajectory. The proposed system has a similar evolution with a transform function that aggressively tracks the increasing power of different assets. As a result, the better performing assets will receive more investment. The proposed PPT objective can be formulated as a fast backpropagation algorithm, which is suitable for large-scale and time-limited applications, such as high-frequency trading. Extensive experiments on several benchmark data sets from diverse real financial markets show that PPT outperforms other state-of-the-art systems in computational time, cumulative wealth, and risk-adjusted metrics. It suggests that PPT is effective and even more robust than some defensive systems in PS.