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By considering the stock market’s fuzzy uncertainty and investors’ psychological factors, this paper studies the portfolio performance evaluation problems with different risk attitudes (optimistic, pessimistic, and neutral) by the Data Envelopment Analysis (DEA) approach. In this work, the return rates of assets are characterized as trapezoidal fuzzy numbers, whose membership functions with risk attitude parameters are described by exponential expression. Firstly, these characteristics with risk attitude are strictly derived including the possibilistic mean, variance, semi-variance, and semi-absolute deviation based on possibility theory. Secondly, three portfolio models (mean-variance, mean-semi-variance, and mean-semi-absolute-deviation) with different risk attitudes are proposed. Thirdly, we prove the real frontiers determined by our models are concave functions through mathematical theoretical derivation. In addition, two novel indicators are defined by difference and ratio formulas to characterize the correlation between DEA efficiency and portfolio efficiency. Finally, numerical examples are given to verify the feasibility and effectiveness of our model. No matter what risk attitude an investor holds, the DEA can generate approximate real frontiers. Correlation analysis indicates that our proposed approach outperforms in evaluating portfolios with risk attitudes. At the same time, our model is an improvement of Tsaur’s work (2013) which did not study the different risk measures, and an extension of Chen et al.’s work (2018) which only considered risk-neutral attitude.

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Portfolio is primarily focused on its future returns and investment allocations. On the one hand, GARCH-EVT-Copula is increasingly proved to have outstanding advantages in improving the accuracy of predicting returns. On the other hand, researchers pay more attention to investor sentiment described by four indexes, namely, market turnover ratio, advance decline ratio, new highs/lows ratio, and ARMS index. Therefore, considering the two factors mentioned above, we propose an ARMA-GARCH-Sent-EVT-Copula portfolio model with investor sentiment. Firstly, the investor sentiment indicator is constructed by principal component analysis, which is added to the time series model to obtain the ARMA-GARCH-Sent model. Considering the advantages of extremum theory, we present the ARMA-GARCH-Sent-EVT model to describe the daily logarithmic return series of stocks. Secondly, the Copula model is used to construct the multivariate distribution of daily logarithmic stock return series to capture their asymmetric and nonlinear characteristics. Furthermore, in order to highlight the advantages of our model, we make a comparative analysis of three models: the original ARMA-GARCH-Copula model, the ARMA-GARCH-Sent-Copula model and the ARMA-GARCH-Sent-EVT-Copula model. Finally, we use the data of SSEC and SZI for empirical analysis and compare the dynamic portfolio strategies of the three models, respectively. The results show that our model with investor sentiment is superior to the other two models in terms of maximum Sharpe ratio and mean-variance optimization, that is, it has higher returns under the same conditions.

The classical Analytic Hierarchy Process (AHP) requires an exact value to compare the relative importance of two attributes, but experts often can not obtain an accurate assessment of every attribute in the decision-making process, there are always some uncertainty and hesitation. Compared with classical AHP, our new defined interval-valued intuitionistic fuzzy AHP has accurately descripted the vagueness and uncertainty. In decision matrix, the real numbers are substituted by fuzzy numbers. In addition, each expert will make different evaluations according to different experiences for each attribute in the subjective weighting method, which neglects objective factors and then generates some deviations in some cases. This paper provides two ways to make up for this disadvantage. On the one hand, by combining the interval-valued intuitionistic fuzzy AHP with entropy weight, an improved combination weighting method is proposed, which can overcome the limitations of unilateral weighted method only considering the objective or subjective factors. On the other hand, a new score function is presented by adjusting the parameters, which can overcome the invalidity of some existing score functions. In theory, some theorems and properties for the new score functions are given with strictly mathematical proof to validate its rationality and effectiveness. In application, a novel fuzzy portfolio is proposed based on the improved combination weighted method and new score function. A numerical example shows that these results of our new score function are consistent with those of most existing score functions, which verifies that our model is feasible and effective.