Uncertain Portfolio Selection Research Articles

A novel probabilistic risk measure model for multi-period uncertain portfolio selection

A novel probabilistic risk measure model for multi-period uncertain portfolio selection

Modeling of linear uncertain portfolio selection with uncertain constraint and risk index

Modeling of linear uncertain portfolio selection with uncertain constraint and risk index

Mean-risk model for uncertain portfolio selection with background risk and realistic constraints

<p style='text-indent:20px;'>This paper studies a portfolio selection problem in such a situation where the future asset return rates cannot be well obtained by historical data but have to be given by experts' evaluations. In order to reflect the impact of realistic conditions on investment decisions, background risk and some realistic constraints are also considered. First, a nonlinear uncertain mean-risk model for uncertain portfolio selection is proposed. For further discussion, the crisp equivalent forms of the model are presented. Then, an effective solution method for solving the model is obtained. Furthermore, the influence of background risk on investment strategies is discussed by comparing the optimal expected return with background risk with that without background risk. Finally, some numerical examples are provided to illustrate the performance and applications of the model.</p>

Multi-period uncertain portfolio selection model with prospect utility function.

In this paper, we discuss a multi-period portfolio optimization problem based on uncertainty theory and prospect theory. We propose an uncertain multi-period portfolio selection model, in which the return utility and risk of investment are measured by prospect theory utility function and uncertain semivariance. More realistically, the influence of transaction costs and bankruptcy of investor are also considered. Moreover, to solve the portfolio model, this paper designs a new artificial bee colony algorithm by combining sine cosine search method. Finally, a numerical experiment is presented to demonstrate the proposed model and the effectiveness of the designed algorithm.

Uncertain minimax mean-variance and mean-semivariance models for portfolio selection1

Traditionally, the return on investment has been described as either a random variable or a fuzzy variable, while this paper discusses the uncertain portfolio selection in which each security return is assumed to be an uncertain variable. To better optimize the return and risk of a portfolio, we propose two models: uncertain minimax mean-variance (UM-EV) model and uncertain minimax mean-semivariance (UM-SVE) model. The crisp equivalents of the UM-EV model that regard the security return as a normal and linear uncertain variable are derived, and the optimization problem is solved using linear programming. For the UM-SVE model, the crisp equivalent of a zigzag uncertain variable is introduced, and the optimization solution is calculated using hybrid intelligent algorithm. Finally, the effectiveness of the proposed models is illustrated using numerical examples.

Modeling of Linear Uncertain Portfolio Selection with Uncertain Constraint and Risk Index

Modeling of Linear Uncertain Portfolio Selection with Uncertain Constraint and Risk Index

Uncertain portfolio selection model with stock index and put option

Uncertain portfolio selection model with stock index and put option

An analytic solution for multi-period uncertain portfolio selection problem

An analytic solution for multi-period uncertain portfolio selection problem

A risk index model for uncertain portfolio selection with background risk

This study proposes a new uncertain risk index model with background risk and presents its deterministic equivalents. The security returns and background asset returns are assumed as uncertain variables and estimated by experts. To discuss the influence of background risk on investment decisions, we compare the proposed model with a variant without background risk and find that the portfolio with background risk produces an equal or lower return than the one without background risk. The effects of changes in the standard deviation of background asset and the risk-free interest rate on optimal expected value are discussed. Two different risk measures for portfolio optimization model with background risk are compared, viz., the risk index model with background risk is further compared with the mean chance model with background risk. The nonlinear risk index model is solved by using a genetic algorithm. The efficiency of the genetic algorithm and the applications of the proposed models are illustrated through numerical experiments.

Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns

Diversification portfolio selection problem is an important issue in uncertain economic environment. In this paper, this problem is discussed within the framework of uncertainty theory. First, an uncertain extension mean-variance diversification model is proposed, in which the mean is chosen as the objective function, and variance and proportion entropy as risk and diversity constraints. Then two variations are investigated on the purposes of minimizing the risk and maximizing the diversity measure, respectively. Furthermore, the corresponding analytical mathematical models are deduced via the convenient operational law of uncertain variables. Finally, several numerical examples are given to illustrate the modeling idea. The results showed that the diversification models had higher diversification than the uncertain mean-variance model. The proposed models provide a new method to make decision-making in uncertain portfolio selection problem.

Uncertain portfolio selection with mental accounts

Since the security market is so complex, in real life, there are situations where the future security returns cannot be reflected by the past data and are given by experts' estimations according to their knowledge and judgement rather than by historical data. This paper discusses a portfolio selection problem in such an uncertain environment. In the paper, in order to reflect different attitudes towards risk that vary by goal in one portfolio investment, we apply mental account to the investment. Using uncertainty theory, we propose a new mean–variance uncertain portfolio selection model with mental accounts. Furthermore, we discuss the shape of the mean–standard deviation efficient frontier of the subportfolios of each mental account when security returns are normal uncertain variables and further give the condition where the optimal aggregate portfolio is on the mean–standard deviation efficient frontier. In addition, we compare the optimal portfolio with mental accounts with that without mental accounts. Finally, a numerical example is given as an illustration.

Uncertain Portfolio Selection with Borrowing Constraint and Background Risk

Due to the complexity of financial markets, there exist situations where security returns and background factor returns are available mainly based on experts’ subjective beliefs, such as in the case of lack of historical data. To deal with such indeterminate quantities, uncertain variables are introduced. Based on uncertainty theory, this paper discusses the distribution function of the optimal portfolio return. Two types of new uncertain programming models, namely, the chance-mean model and the measure-mean model, are proposed to make an optimal portfolio selection decision in an uncertain environment. It is proved that there exists an equivalent relation between the chance-mean model and a deterministic linear programming model, which leads to an approach to obtain the optimal solutions of the proposed models. Finally, some numerical examples are illustrated to show the modelling ideas and the effectiveness of the models.

损失厌恶下的多期多目标不确定投资组合模型及算法

损失厌恶下的多期多目标不确定投资组合模型及算法

Research and comparison of uncertain portfolio selection model with background risk and mental accounts

Research and comparison of uncertain portfolio selection model with background risk and mental accounts

A multi-period regret minimization model for uncertain portfolio selection with bankruptcy constraint

A multi-period regret minimization model for uncertain portfolio selection with bankruptcy constraint

Uncertain portfolio selection with mental accounts and background risk

In real life, investors face background risk which may affect their portfolio selection decision. In addition, since the security market is too complex, there are situations where the future security returns cannot be reflected by historical data and have to be given by experts' estimations according to their knowledge and judgement. This paper discusses a portfolio selection problem with background risk in such an uncertain environment. In the paper, in order to reflect different attitudes towards risk that vary by goal in one portfolio investment, we apply mental accounts to the investment. Using uncertainty theory, we propose an uncertain portfolio selection model with mental accounts and background risk and provide the determinate form of the model. Moreover, we discuss the shape and location of efficient frontier of the subportfolios with background risk and without background risk. Further, we present the conditions under which the optimal aggregate portfolio is on the efficient frontier when return rates of security and background asset are all normal uncertain variables. Finally, a real portfolio selection example is given as an illustration.

Uncertain portfolio selection with mental accounts and realistic constraints

Since the security market is too complex, there are situations where the future security returns cannot be reflected by historical data and have to be given by experts’ estimations according to their knowledge and judgements. This paper discusses a portfolio selection problem in such an uncertain environment. In the paper, in order to reflect different attitudes towards risk that vary by goal in one portfolio investment, we apply mental accounts to the investment. Uncertain variables are introduced to describe the securities’ return, and a new uncertain portfolio selection model is developed when return risk control and liquidity risk control are considered. In addition, other important limitations, i.e., transaction cost, minimum transaction lot, bounds of holding, security diversification and sector diversification are also considered. In real life, investors face background risk which may affect their portfolio selection decisions. Thus, background risk is also considered. To solve the proposed problem, the equivalents of the model are proposed. Finally, a numerical example is given as an illustration.

Multi-period and tri-objective uncertain portfolio selection model: A behavioral approach

This paper discusses a multi-period and tri-objective portfolio optimization problem, where asset returns are formalized as uncertain variables. Based on uncertainty theory, a multi-period and tri-objective uncertain portfolio model is proposed, which considers the loss-averse utility, liquidity risk and diversification degree simultaneously. Additionally, a chance constraint is introduced into the model to reflect investors’ safety requirement during the investment period. To solve the portfolio model, a self-adaptive particle swarm optimization (SAPSO) is also proposed. In SAPSO, a self-adaptive stochastic ranking approach is employed to balance the abilities of exploration and exploitation in the searching process. Finally, a numerical experiment is presented. The results show that SAPSO is effective to solve the proposed model and the proposed portfolio model can express investors’ preference by adjusting the objective weights.

Multiperiod mean absolute deviation uncertain portfolio selection with real constraints

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. Most of existing mean---absolute deviation models are devoted to stochastic single-period portfolio optimization. However, practical investment decision problems often involve the uncertain dynamic information. Considering transaction costs, borrowing constraints, threshold constraints, cardinality constraints and risk control, we present a novel multiperiod mean absolute deviation uncertain portfolio selection model, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. In proposed model, the return rate of asset and the risk are quantified by uncertain expected value and uncertain absolute deviation, respectively. Cardinality constraints limit the number of risky assets in the optimal portfolio. Threshold constraints limit the amount of capital to be invested in each asset and prevent very small investments in any asset. Based on uncertainty theories, the model is transformed into a crisp dynamic optimization problem. Because of the transaction costs and cardinality constraints, the multiperiod portfolio selection is a mix integer dynamic optimization problem with path dependence, which is "NP hard" problem that is very difficult to solve. The proposed model is approximated to a mix integer dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy and is proved linearly convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

A Risk-Free Protection Index Model for Multi-Objective Uncertain Portfolio Selection with Entropy and Variance Constraints

A Risk-Free Protection Index Model for Multi-Objective Uncertain Portfolio Selection with Entropy and Variance Constraints