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Traditional portfolio selection models mainly obtain the optimized portfolio ratio by focusing on the prices of financial products. However, investors’ multiple preferences and risk appetites are also significant factors that should be taken into account. In consideration of these two factors simultaneously, we propose a double-hierarchy model in this paper. Specifically, the first hierarchy quantifies investors’ risk appetite based on a historical simulation method and probabilistic preference theory. This hierarchy can be utilized to describe investors’ variable risk appetites and ensure the obtained investment ratios meet investors’ immediate risk requirements. Then, using the cross-efficiency evaluation principle, the optimal investment ratios can be derived by fusing investors’ multiple preferences and risk appetites in the second hierarchy. Lastly, an illustrative example about evaluating the 10 largest capitalized stocks on the Shenzhen Stock Exchange is given to verify the feasibility and effectiveness of our newly proposed model. We make the theoretical contribution to improve the traditional portfolio selection model, especially considering investors’ subjective preferences and risk appetite. Moreover, the proposed model can be practical for assisting investors with their investment strategies in real life.

Portfolio Selection with respect to the Probabilistic Preference in Variable Risk Appetites: A Double-Hierarchy Analysis Method