Possibilistic Mean-variance Model Research Articles

The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions

The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model.

Management optimization of nonpoint source pollution considering the risk of exceeding criteria under uncertainty

Management of nonpoint source (NPS) pollution is highly important in watershed water environmental and ecological security. However, the many complexities and uncertainties that exist in the processes of export and management of NPS pollution exert substantial influences on the reliability of multiple management practices. This study developed an inexact multiobjective possibilistic mean-variance mixed-integer programming (IMPMMP) model for NPS pollution management through optimization of watershed land use pattern and livestock production structure. By coupling interval parameter programming, mixed-integer programming, multiobjective programming, and an export coefficient model within a general possibilistic mean-variance model framework, the IMPMMP model deals effectively with system uncertainties and complexities. Moreover, the risk of exceeding criteria (REC) in NPS pollution management systems can be considered. The proposed IMPMMP model was applied to a real-world case study in the Xinfengjiang Reservoir watershed in South China. Results showed that the preference of decision makers regarding land use adjustment plays a decisive role in determining model feasibility. The area provided for each land use type that could be adjusted has to reach a certain threshold to achieve the goals of reduced pollution load and REC control. The NPS pollution loads after optimization would be exported primarily from different land uses and the human population. Compared with NPS nitrogen pollution management, it is more difficult to reduce the NPS phosphorus load and to manage the corresponding REC through adjustment of the land use pattern and livestock production structure. Moreover, it is difficult to simultaneously reduce the NPS nitrogen and phosphorus pollution loads and REC in each subbasin. The model, which can provide policy makers with a series of schemes for optimization of land use pattern and livestock production structure, has satisfactory applicability and could be used for watershed NPS pollution management.

Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States

In previous studies, there were few portfolio models involving investors’ psychological states, market ambiguity and entropy. Some entropy can make the model have the effect of diversifying investment, which is very important. This paper mainly studies four kinds of entropy. First, we obtained four definitions of entropy from the literature, and gave the function of fuzzy entropy in different psychological states through strict mathematical proof. Then, we construct a fuzzy portfolio entropy decision model based on the investor’s psychological states, and compared it with the possibilistic mean–variance model. Then we presented a numerical example and compared the five different models established. By comparing the results, we find that: (a) The possibilistic mean–Shannon entropy model solves the problem of the possibility of excessive concentration in the possibilistic mean–variance model, but the dispersion is not enough. Conversely, the possibilistic mean–Yager entropy is over–emphasized due to the definition of its own function, such that it gave an investment pattern of equal weight distribution or approximate average distribution. (b) The results of possibilistic mean–proportional entropy can be said to be the middle status of the portfolios of possibilistic mean–Shannon entropy and possibilistic mean–Yager entropy. This portfolio not only achieves a certain rate of return, but also disperses the risk to some extent. (c) The lines of satisfaction for portfolios derived from different models are approximately U–shaped with the increase in return preference. (d) The possibilistic mean–Shannon entropy model tends to have the highest portfolio satisfaction with the same psychological state of the investor.

A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection

The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributions on the portfolio selection with VaR constraint and risk-free investment considering real data. The results showns that were not difference in assets selection and in return rate, however, There was a change in the risk rate, which was higher in the Laplace distribution than in the normal distribution.

Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment

We propose a possibilistic portfolio model with VaR constraint and risk-free investment based on the possibilistic mean and variance, while assuming that the expected rate of returns is a fuzzy number. The model shows more clearly that, in the financial market affected by several non-probabilistic factors, risk-averse investors wish not only to reach the expected rate of returns in their actual investment, but also to assure that the maximum of their possible future risk is lower than an expected loss. Under the condition that the expected rate of returns is a normal distribution fuzzy variable, we proposed a theorem as the solution, and derive a crisp equivalent form of the possibilistic portfolio under constraints of VaR and risk-free investment. This model is an expansion of the fuzzy possibilistic mean–variance model by Zhang (2007). Finally, an empirical study is carried out using the data concerning some stocks of various industries listed at the Shanghai Stock Exchange. A conclusion is reached that the investors are able to choose a portfolio more suitable to them under the VaR constraint.

A fuzzy portfolio selection method based on possibilistic mean and variance

This paper deals with the portfolio selection problem when the returns of assets obey LR-type possibility distributions and there exist the limits on holdings. A new possibilistic mean–variance model to portfolio selection is proposed based on the definitions of the possibilistic return and possibilistic risk, which can better integrate an uncertain decision environment with vagueness and ambiguity. This possibilistic mean–variance model can be regarded as extensions of conventional probabilistic mean–variance methodology and previous possibilistic approaches since it contains less parameter and has a more extensive application. A numerical example of a possibilistic fuzzy portfolio selection problem is given to illustrate our proposed effective means and approaches.