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In the traditional portfolio models, the return rates of risky assets are usually defined as random variables or fuzzy variables. However, when some events such as financial crises or wars occur that can cause instability in financial markets, the results of these assumptions are not always satisfactory. Therefore, some scholars try to use uncertain variables to express the return rates. In this paper, a two-factor uncertain portfolio problem under optimistic value criteria is studied, where we use the optimistic value instead of expected value to describe the investment return and study the impact of economic circumstance factor and corporation's specificity factor on the return rates. Firstly, a two-factor optimistic value-variance-entropy model with background risk is constructed, in which the total investment return consists of the risky asset return and the background asset return. Then, considering the investors with two kinds of risk preferences, a three-step method is applied to convert the bi-objective optimization model. Moreover, a moment estimation method is used to process the expert-estimated data on the return rates. Finally, a numerical simulation is presented for showing the applicability of our models and solution method. • We use optimistic value to represent the return rather than expected value. • The multiple factors and background risk are considered simultaneously. • Three-step method is used to convert the model into two single-objective models. [ABSTRACT FROM AUTHOR]

With the development of financial market, people invest their savings into different financial products to increase return. However, financial market is an extremely complex system, where investment opportunities and risk often coexist. For investors, it is necessary to take effective measures to avoid risk while obtaining considerable return. In recent decades, actively managing investment in the form of a portfolio is widely accepted by investors. In this paper, we propose a new three-objective Sortino ratio-expected shortfall-turnover rate (SR-ES-TR) portfolio optimization (PO) model. The Sortino ratio is used to measure the risk-adjusted rate of return. The expected shortfall is used to measure the tail risk of a portfolio. Portfolio liquidity risk is characterized by turnover rate. We constructed a portfolio of ten stocks and solved the SR-ES-TR model by the novel MOPSO-SODE algorithm. Compared with other four multi-objective algorithms, the better performance and validity in solving SR-ES-TR model by MOPSO-SODE algorithm have been verified. • Established a three-objective SR-ES-TR portfolio optimization model with liquidity ratio. • Designed a MOPSO-SODE algorithm based on the MOPSO framework. • Verified the effectiveness of the MOPSO-SODE algorithm in solving SR-ES-TR model. [ABSTRACT FROM AUTHOR]

• A cloud theory-based multi-objective portfolio selection model is proposed. • The crisp numerical characteristics of the cloud model theory are defined. • The acceptance and rejection functions with variable risk appetite are constructed. • A compromise programming approach is utilized to aggregate the objectives. • Several schemes as per investors' preferences regarding all objectives are devised. This study proposes a cloud theory-based multi-objective portfolio selection model with variable risk appetite, which incorporates four objectives of mean, variance, skewness, and liquidity constrained by several realistic constraints. Cloud model theory is employed to characterize the return rates and liquidity of assets due to the superiority of simultaneously capturing the ambiguity and randomness of information. The crisp numerical characteristics of the cloud model are defined to obtain the crisp form of the proposed model. To highlight and portray the investors' risk (averse-neutral-seeking) appetites, the generalized acceptance and rejection functions are modeled by using the extreme values of each objective and introducing a variable risk appetite parameter. Thus the corresponding model is transformed with the objective functions of maximizing acceptance and minimizing rejection, which is solved through the compromise programming approach. The extended model provides investors with an opportunity to adjust risk parameters according to current market status. Moreover, the preference ratio vector is introduced when optimizing, which provides investors with overall control over the preferences regarding all objectives, so that investors can derive optimal portfolios well compatible with their expectations through customized weighting schemes. A real-world empirical application is presented to demonstrate the effectiveness of the proposed model [ABSTRACT FROM AUTHOR]