Mathematical Foundations of Computing doi:10.3934/mfc.2023043 DISTRIBUTIONALLY ROBUST SPARSE PORTFOLIO OPTIMIZATION MODEL UNDER SATISFACTION CRITERION Zhongyan Wang 1,2,3 , Xiaodong Zhu ∗1,2,3 , Shaojian Qu 1,2,3 , M. Faisal Nadeem 4 and Beibei Zhang 5 1 The Research Institute for Risk Governance and Emergency Decision-Making Nanjing University of Information Science and Technology, Nanjing 210044, China 2 School of Management Science and Technology Nanjing University of Information Science and Technology, Nanjing 210044, China 3 Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters(CIC-FEMD) Nanjing University of Information Science and Technology, Nanjing, China 4 Department of Mathematics, COMSATS University Islamabad Lahore Campus, Lahore 54000, Pakistan 5 School of Economics and Management, Anhui Jianzhu University, Hefei, China Abstract. We propose a distributionally robust portfolio optimization model with cardinality constraints under the satisfaction criterion. We aim to max- imize the probability of achieving the target return of the proposed portfolio selection model while the number of assets the investors hold is limited. For practical significance, we cite a measure of shortfall-aware aspiration level to the portfolio optimization problem and convert it into a CVaR measure. In our model, we consider a worst-case and assume the distribution of returns of assets is ambiguous. We reformulate the CVaR-based measure equivalently to semi-definite programming for its tractability. A Benders’ decomposition algo- rithm is designed to solve the proposed model efficiently. Numerical tests are utilized through actual market data to validate the proposed method. The re- sults indicate that our algorithm can effectively solve the proposed model, and the sparse portfolio selection model under the satisfaction criterion achieves high robustness and perform better than classical models. Furthermore, we prove that taking the number of assets as the decision variable is a much more efficient method. 1. Introduction. The satisfaction criterion has played a significant role in many fields, especially in the area of decision making, see Zopounidis et al. [37] and Yager et al. [33]. The classical portfolio selection model aim to maximize the expected return to attain optimality criterion, which can be unrealistic. Faced with various complicated, uncertain situations, the limitation of information restricts the scope of choice and the specific grasp of the state of investors. Therefore, it is more practical for investors to choose satisfaction criteria to make decisions. In fact, in the investment territory, the decisions that investors make are often 2020 Mathematics Subject Classification. Primary: 90C17, 90C15; Secondary: 90C29. Key words and phrases. Satisfaction criterion, sparse portfolio selection, distributionally robust optimization, Benders’ decomposition. ∗ Corresponding author: Xiaodong Zhu. 1