# Stock Portfolio Management in the Presence of Downtends Using Computational Intelligence
## 3 Literature Review
### Portfolio Management: Price Forecasting, Stock Selection and Portfolio Optimization  
In recent years, there have been plenty of contributions on price forecasting based on either statistical or computational intelligence methods (see [10, 27]). The stock market is characterized by extreme fluctuations, non-linearity, and shifts in internal and external environmental variables. Artificial intelligence techniques can detect such non-linearity, resulting in much-improved forecast results [28].  
Among the computational intelligence methods used for price forecasting are deep learning (e.g., [29, 30, 31, 32]) and machine learning (e.g., [33, 34, 35]). In [10], a hybrid stock selection model with a stock prediction stage based on an artificial neural network (ANN) trained with the extreme learning machine (ELM) training algorithm ([6, 36]) was proposed. The ELM algorithm has been tested for financial market prediction in other works (see [7, 8, 9]).  
There are important works on methods for stock selection, which have several different fundamental theories, from operations research methods (e.g., [37, 38]) to approaches originating in modern portfolio theory (Mean-variance model) (e.g., [38, 39]) and soft computing methods (e.g., [40, 41]), including hybrid approaches (e.g., [10, 42, 43]).  
The fundamental theory for portfolio optimization is [PERSON]'s mean-variance model ([44]). Its formulation marked the beginning of Modern portfolio theory ([45]). However, [PERSON]'s original model is considered too basic since it neglects real-world issues related to investors, trading limitations, portfolio size and others ([43]). For evaluating a portfolio's performance, the model is based on measuring the expected return and the risk; the latter is represented by the variance in the portfolio's historical returns. Since the variance takes into account both negative and positive deviations, other risk measures have been proposed, such as the Conditional Value at Risk (CVaR) ([46, 47]). As a result, numerous works have improved the model, creating more risk measures and proposing restrictions that bring them closer to practical aspects of stock market trading ([27]). Consequently, many optimization methods based on exact algorithms (e.g., [48, 49, 50, 51, 52, 53, 54, 55]) and heuristic and hybrid optimization (e.g., [56, 57, 58, 59, 60, 61, 62, 63, 64, 65]) have been proposed to solve the emerging portfolio optimization models ([27, 40, 45]).  
According to [12], the investor or decision maker in the portfolio selection problem manages a multiple criteria problem in which, along with the objective of return maximization, he/she faces the uncertainty of risk. Different attitudes assumed by decision makers may lead them to select different alternatives. A way of modeling both risk and subjectivity of the decision maker in terms of significant confidence intervals was first proposed in [12]. The probabilistic confidence intervals of the portfolio returns characterize the portfolios during the optimization. The optimization is performed by means of a widely accepted decomposition-based evolutionary algorithm, the MOEA/D ([25, 66]). This approach is inspired on the independent works of ([67, 68]) on interval analysis theory.