Uncertain Portfolio Selection Research Articles

Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint

• A multi-period uncertain portfolio selection problem is discussed. • A new method is presented for modeling the multi-period uncertain portfolio selection problem. • A deterministic transformation method is proposed for solving problem. The complexity of financial markets leads to different types of indeterminate asset returns. For example, asset returns are considered as random variables, when the available data is enough. When the available data is too small or even no available data to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degrees of asset returns. Then, asset returns can be described as uncertain variables. In this paper, we discuss a multi-period portfolio selection problem under uncertain environment, which maximizes the final wealth and minimizes the risk of investment. Unlike the common method to describe the multi-period portfolio selection problem as a bi-objective optimization model, we formulate this uncertain multi-period portfolio selection problem by a new method in three steps with two single objective optimization models. And, we consider the influence of transaction cost and bankruptcy of investor. Then, the proposed uncertain optimization models are transformed into the corresponding crisp optimization models and we use the genetic algorithm combined with penalty function method to solve them. Finally, a numerical example is given to show the effectiveness and practicability of proposed models and method.

Uncertain portfolio selection with high-order moments

Uncertain portfolio selection with high-order moments

Mean-risk model for uncertain portfolio selection with background risk

When making investment decisions, one will face not only the risk of financial assets within portfolio but also background risk. This paper discusses an uncertain portfolio selection problem in which background risk is considered and the security returns and background assets return are given by experienced experts’ evaluations instead of historical data. Regarding the returns of the securities and background assets as uncertain variables, we propose an uncertain mean-risk model with background risk for portfolio selection and the crisp forms of the model are provided when security returns obey different uncertainty distributions. In addition, when everything else is same, it is concluded that the optimal expected return of the mean-risk model with background risk is usually smaller than that without background risk. Moreover, the relationship between the optimal solution of our model and that of the model in Huang’s paper “Uncertain Portfolio Selection with Background Risk” is discussed. Finally, numerical examples are presented to illustrate the effectiveness of the model and to show the effect of background risk on investment decision.

A review of uncertain portfolio selection

This paper reviews the theory of uncertain portfolio selection which uses human estimates as inputs and applies uncertainty theory to select portfolios. The difference of the uncertain portfolio selection theory from the stochastic portfolio theory is given and the necessity and conditions for usin g the theory are presented. Some basic works are introduced, including different types of mathematical risk measurements, their features, and some basic uncertain portfolio selection models and their theorems. Finally, future work for uncertain portfolio selection is discussed.

Uncertain portfolio selection model considering transaction costs and minimum transaction lots requirement

Uncertain portfolio selection model considering transaction costs and minimum transaction lots requirement

Cross-entropy based multi-objective uncertain portfolio selection problem

Cross-entropy based multi-objective uncertain portfolio selection problem

Uncertain Portfolio Selection with Background Risk and Liquidity Constraint

This paper discusses an uncertain portfolio selection problem with consideration of background risk and asset liquidity. In addition, the transaction costs are also considered. The security returns, background asset return, and asset liquidity are estimated by experienced experts instead of historical data. Regarding them as uncertain variables, a mean-risk model with background risk, liquidity, and transaction costs is proposed for portfolio selection and the crisp forms of the model are provided when security returns obey different uncertainty distributions. Moreover, for better understanding of the impact of background risk and liquidity on portfolio selection, some important theorems are proved. Finally, numerical experiments are presented to illustrate the modeling idea.

Multiperiod mean semi-absolute deviation interval portfolio selection with entropy constraints

In this paper, we discuss the uncertain portfolio selection problem where the asset returns are represented by interval data. Since the parameters are interval values, the gain of returns is interval value as well. A new multiperiod mean semi-absolute deviation interval portfolio selection model with the transaction costs, borrowing constraints, threshold constraints and diversification degree of portfolio has been proposed, where the return and risk are characterized by the interval mean and interval semi-absolute deviation of return, respectively. The diversification degree of portfolio is measured by the presented possibilistic entropy. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on interval theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. The discrete approximate iteration method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of differently desired number of assets and different preference coefficients are provided by numerical examples to illustrate the efficiency of the proposed approach and the designed algorithm.

Portfolio selection models based on Cross-entropy of uncertain variables

This paper researches the uncertain portfolio selection problem when security returns are hard to be well reflected by previous data. We take security returns as uncertain variables. Firstly, three new portfolio selection models are presented based on the cross-entropy of uncertain variables. Secon dly, the crisp form of the new model is also provided when security returns are linear uncertain variables. In addition, the gravitation search algorithm and numerical integration are introduced to solve the proposed models. Finally, several numerical examples are presented to illustrate the effectiveness of the algorithm and the application of the mathematical models.

Diversified models for portfolio selection based on uncertain semivariance

ABSTRACTSince the financial markets are complex, sometimes the future security returns are represented mainly based on experts’ estimations due to lack of historical data. This paper proposes a semivariance method for diversified portfolio selection, in which the security returns are given subjective to experts’ estimations and depicted as uncertain variables. In the paper, three properties of the semivariance of uncertain variables are verified. Based on the concept of semivariance of uncertain variables, two types of mean-semivariance diversified models for uncertain portfolio selection are proposed. Since the models are complex, a hybrid intelligent algorithm which is based on 99-method and genetic algorithm is designed to solve the models. In this hybrid intelligent algorithm, 99-method is applied to compute the expected value and semivariance of uncertain variables, and genetic algorithm is employed to seek the best allocation plan for portfolio selection. At last, several numerical examples are presented to illustrate the modelling idea and the effectiveness of the algorithm.

Multiperiod Mean Absolute Deviation Uncertain Portfolio Selection

Multiperiod portfolio selection problem attracts more and more attentions because it is in accordance with the practical investment decision-making problem. However, the existing literature on this field is almost undertaken by regarding security returns as random variables in the framework of probability theory. Different from these works, we assume that security returns are uncertain variables which may be given by the experts, and take absolute deviation as a risk measure in the framework of uncertainty theory. In this paper, a new multiperiod mean absolute deviation uncertain portfolio selection models is presented by taking transaction costs, borrowing constraints and threshold constraints into account, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on uncertain theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. To solve the new model in general cases, the forward dynamic programming method is presented. In addition, a numerical example is also presented to illustrate the modeling idea and the effectiveness of the designed algorithm.

Uncertain portfolio selection with background risk

In real life, investors face background risk which may affect their portfolio selection decision. In addition, there are situations where background asset return and the security returns have to be given by experts’ evaluations because of occurrence of unexpected incidents in economic and social environment or lack of historical data. This paper discusses an uncertain portfolio selection problem in which background risk is considered and the returns of the securities and the background assets are given by experts’ evaluations instead of historical data. Using uncertainty theory, we propose a new uncertain portfolio selection model with background risk. To enable the users to solve the problem with currently available programing solvers, the crisp form of the model is provided. In addition, we discuss the optimal solution of the model when the returns of the securities and the background asset return obey normal uncertainty distributions, and compare the optimal portfolio with background risk with that without background risk. It is concluded that when everything else is same, the expected optimal portfolio return with background risk is smaller than that without background risk. Finally, a numerical example is given as an illustration.

An artificial bee colony algorithm for uncertain portfolio selection.

Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts' evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm.

A risk index model for multi-period uncertain portfolio selection

This paper discusses a multi-period portfolio selection problem when security returns are given by experts’ evaluations. The security return rates are regarded as uncertain variables and an uncertain risk index adjustment model is proposed. Optimal portfolio adjustments are determined with the objective of maximizing the total incremental wealth within the constraints of controlling the cumulative risk index value over the investment horizon and satisfying self-financing at each period. To enable the users to solve the model problem with currently available programming tools, an equivalent of the model is provided. In addition, a method of obtaining the uncertainty distributions of the security returns is given based on experts’ evaluations, and a selection example is presented.

The mean-absolute deviation portfolio selection problem with interval-valued returns

In real-world investments, one may care more about the future earnings than the current earnings of the assets. This paper discusses the uncertain portfolio selection problem where the asset returns are represented by interval data. Since the parameters are interval valued, the gain of returns is interval valued as well. According to the concept of the mean-absolute deviation function, we construct a pair of two-level mathematical programming models to calculate the lower and upper bounds of the investment return of the portfolio selection problem. Using the duality theorem and applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a conventional one-level mathematical program. Solving the pair of mathematical programs produces the interval of the portfolio return of the problem. The calculated results conform to an essential idea in finance and economics that the greater the amount of risk that an investor is willing to take on the greater the potential return.

Mean-risk model for uncertain portfolio selection

This paper discusses the uncertain portfolio selection problem when security returns cannot be well reflected by historical data. It is proposed that uncertain variable should be used to reflect the experts' subjective estimation of security returns. Regarding the security returns as uncertain variables, the paper introduces a risk curve and develops a mean-risk model. In addition, the crisp form of the model is provided. The presented numerical examples illustrate the application of the mean-risk model and show the disaster result of mistreating uncertain returns as random returns.

A novel algorithm for uncertain portfolio selection

In this paper, the conventional mean–variance method is revised to determine the optimal portfolio selection under the uncertain situation. The possibilistic area of the return rate is first derived using the possibisitic regression model. Then, the Mellin transformation is employed to obtain the mean and the risk by considering the uncertainty. Next, the revised mean–variance model is proposed to deal with the problem of uncertain portfolio selection. In addition, a numerical example is used to demonstrate the proposed method. On the basis of the numerical results, we can conclude that the proposed method can provide the more flexible and accurate results than the conventional method under the uncertain portfolio selection situation.