Modeling Investor Risk Perception in Qualitative Financial Portfolio Optimization Processes: Preference Driven and Interaction-Based Approaches

Abstract Quantitative portfolio optimization methods are mainly based on precise numerical inputs and complete historical data. However, accessing complete historical data in real-world investment environments is not easy; often, the data are ambiguous and/or have qualitative characteristics. At this point, the use of qualitative portfolio optimization methods gains importance. This study introduces novel qualitative financial portfolio optimization approaches that integrate non-additive measures and the Shapley value to model uncertainty and interaction effects among assets for investment decision-making. By incorporating hesitant fuzzy sets, the proposed approach systematically captures subjective investor judgments, linguistic evaluations, and ambiguous data, thus allowing for personalized risk modeling. The framework distinguishes two levels of interaction: (i) Criterion-level interdependencies, modeled via non-additive measures and Choquet integrals, which enhance the structural consistency of the evaluation process by accounting for synergies and redundancies among decision criteria, and (ii) Asset-level interactions, where Shapley value-derived importance indices identify meaningful combinations of assets. In addition, the model accommodates varying investor profiles by proposing flexible preference functions that reflect different degrees of risk aversion and sensitivity to interactions. In this context, the qualitative portfolio optimization problem is solved according to various investor profiles, and the results are compared with those of established methods. Through comparative analysis, our results demonstrate that explicitly modeling both ambiguity and non-linear interdependencies leads to improved portfolio robustness and better alignment with investor preferences.