The quantity of selected shares with λ = 1.

Portfolio selection and management are two of the most important decisions in the financial field. The existence of uncontrollable factors affects the decision-making process, which is a problem for investors who are responsible for the final financial decisions on how to allocate their budgets to financial assets in their investment portfolios. To overcome the challenges involved in the selection of a stock portfolio, this article presents a three-stage optimization model. In the first stage, the pharmaceutical industry data collected from the Tehran Stock Exchange (TSE) website is used to apply the robust ratio data envelopment analysis (RR-DEA) in GAMS software with respect to some specific financial indicators to determine efficient stocks in conditions of data uncertainty. These selected stocks are then moved to the second stage, where the ANFIS algorithm is employed in MATLAB to predict the final closing prices and calculate the prediction error (RMSE). In the third stage, the fuzzy goal programming (FGP) method is applied, incorporating the prediction errors from the previous stage. The model is optimized in GAMS software, considering each Index’s objectives in a fuzzy context, with the results presented separately for different objectives. For this problem, in the first stage 27 stocks were selected as samples from the (TSE) website using the proposed methods, and 23 stocks were entered into the price prediction stage. Finally, in the FGP stage, optimization and purchase amount of each share was done. Illustrative results show that the proposed approach is effective for portfolio selection and optimization in the presence of uncertain data.

投资组合选择与管理是金融领域最为关键的两类决策。不可控因素的存在会干扰决策流程，这对于最终负责决策如何将预算配置至其投资组合内金融资产的投资者而言，是一项亟待解决的问题。为应对股票投资组合选择过程中面临的挑战，本文提出了一种三阶段优化模型。第一阶段，本文从德黑兰证券交易所（Tehran Stock Exchange, TSE）官网采集医药行业数据，结合特定财务指标，借助GAMS软件实现稳健比率数据包络分析（Robust Ratio Data Envelopment Analysis, RR-DEA），以在数据不确定性环境下筛选出有效股票。经筛选的股票将进入第二阶段，本文在MATLAB中运用自适应神经模糊推理系统（Adaptive Neuro-Fuzzy Inference System, ANFIS）算法对股票最终收盘价进行预测，并计算预测误差（Root Mean Squared Error, RMSE）。第三阶段，本文引入前一阶段得到的预测误差，应用模糊目标规划（Fuzzy Goal Programming, FGP）方法；该模型在GAMS软件中完成优化，兼顾模糊语境下各指标的目标，并针对不同目标分别呈现优化结果。针对本研究问题，本文首先从TSE官网选取27只股票作为样本，经第一阶段方法筛选后，最终有23只股票进入价格预测环节。最终在FGP阶段，完成了各股票的优化配置与购买额度确定。示例结果表明，所提出的方法在存在不确定数据的股票投资组合选择与优化任务中具备有效性。