Investors are concerned about the reliability and safety of their capital, especially its liquidity, when investing. This paper sets up a possibilistic portfolio selection model with liquidity constraint. In this model, the asset return and liquidity are fuzzy variables which follow the normal possibility distributions. Liquidity is measured as the turnover rate of the asset. On the basis of possibility theory, we transform the model into a quadratic programming problem to obtain its solution. We illustrate that, in the process of investment, investors can make better use of capital by choosing their investment portfolios according to their expected return and asset liquidity.

Investor sentiment is a hot topic in behavioral finance. How to measure investor sentiment? Is the influence of investor sentiment on the stock market symmetrical? That is all we need to think about. Therefore, this paper firstly selects five emotional proxy variables and constructs an investor sentiment composite index by principal component analysis. Secondly, the MS-VAR model is employed to study the dynamic relationship among investor sentiment, stock market returns, and volatility. Using the model MSIH (2)-VAR (2), we found that the relationship among the investor sentiment, stock returns, and volatility is different in different regimes. The results of orthogonal cumulative impulse response analysis showed that the shock to investor sentiment has a significant impact on stock market returns, and this impact in the bullish stock market is significantly higher than in the bearish stock market. The impact of the shock to stock market returns on investor sentiment and stock market volatility is relatively significant. The shock to stock market volatility has significant effects on the stock market returns. Overall, the influence of investor sentiment on the stock market is asymmetric; that is, in different regimes of the stock market, the impact of investor sentiment on the stock market is different. Realizing this, investors can better understand and grasp the market, guiding their own investment behavior. Other researchers can also further study the measurement of investor sentiment on this basis to better guide investors’ behavior.

In recent years, fuzzy set theory and possibility theory have been widely used to deal with an uncertain decision environment characterized by vagueness and ambiguity in the financial market. Considering that the expected return rate of investors may not be a fixed real number but can be an interval number, this paper establishes an interval-valued possibilistic mean-variance portfolio selection model. In this model, the return rate of assets is regarded as a fuzzy number, and the expected return rate of assets is measured by the interval-valued possibilistic mean of fuzzy numbers. Therefore, the possibilistic portfolio selection model is transformed into an interval-valued optimization model. The optimal solution of the model is obtained by using the order relations of interval numbers. Finally, a numerical example is given. Through the numerical example, it is shown that, when compared with the traditional possibilistic model, the proposed model has more constraints and can better reflect investor psychology. It is an extension of the traditional possibilistic model and offers greater flexibility in reflecting investor expectations.

Traditional portfolio theory uses probability theory to analyze the uncertainty of financial market. The assets’ return in a portfolio is regarded as a random variable which follows a certain probability distribution. However, it is difficult to estimate the assets return in the real financial market, so the interval distribution of asset return can be estimated according to the relevant suggestions of experts and decision makers, that is, the interval number is used to describe the distribution of asset return. Therefore, this paper establishes a portfolio selection model based on the interval number. In this model, the semiabsolute deviation risk function is used to measure the portfolio’s risk, and the solution of the model is obtained by using the order relation of the interval number. At the same time, a satisfactory solution of the model is obtained by using the concept of acceptability of the interval number. Finally, an example is given to illustrate the practicability of the model.