基于模糊收益率的组合投资模型

本文考虑了收益率为模糊数的投资组合选择问题,利用模型约束简化方差约束,建立了投资组合选择的模糊线性规划模型,然后引进模糊期望把模糊线性规划问题化为普通参数线性规划问题,最后给出了一个数值算例.     

A class of possibilistic portfolio selection model with interval coefficients and its application

Because of the existence of non-stochastic factors in stock markets, several possibilistic portfolio selection models have been proposed, where the expected return rates of securities are considered as fuzzy variables with possibilistic distributions. This paper deals with a possibilistic portfolio selection model with interval center values. By using modality approach and goal attainment approach, it is converted into a nonlinear goal programming problem. Moreover, a genetic algorithm is designed to obtain a satisfactory solution to the possibilistic portfolio selection model under complicated constraints. Finally, a numerical example based on real world data is also provided to illustrate the effectiveness of the genetic algorithm.     

Portfolio selection under possibilistic mean–variance utility and a SMO algorithm

In this paper, we propose a new portfolio selection model with the maximum utility based on the interval-valued possibilistic mean and possibilistic variance, which is a two-parameter quadratic programming problem. We also present a sequential minimal optimization (SMO) algorithm to obtain the optimal portfolio. The remarkable feature of the algorithm is that it is extremely easy to implement, and it can be extended to any size of portfolio selection problems for finding an exact optimal solution.     

A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs

This paper deals with a multi-period portfolio selection problem with fuzzy returns. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection is presented by taking into account four criteria viz., return, risk, transaction cost and diversification degree of portfolio. In the proposed model, the return level is quantified by the possibilistic mean value of return, the risk level is characterized by the lower possibilistic semivariance of return, and the diversification degree of portfolio is measured by the originally presented possibilistic entropy. Furthermore, a hybrid intelligent algorithm is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis between the possibilistic entropy model and the proportion entropy model is provided by two numerical examples to illustrate the efficiency of the proposed approaches and the designed algorithm.     

Weighted portfolio selection models based on possibility theory

In this paper, we discuss portfolio selection problem in a fuzzy uncertain environment. Based on the Fullér’s and Zhang’s notations, we discuss some properties of weighted lower and upper possibilistic means and variances as in probability theory. We further present two weighted possibilistic portfolio selection models with bounded constraint, which can be transformed to linear programming problems under the assumption that the returns of assets are trapezoidal fuzzy numbers. At last, a numerical example is given to illustrate our proposed effective means and approaches.     

带交易费用的投资组合模型的割平面解法

本文讨论了带交易费用的投资组合模型，因对这一类带二次约束的线性优化问题没有特殊的处理方法，我们利用割平面法使这一非线性优化间题可通过解一系列线性规划问题来求解．     

带交易费用的证券组合投资选择的优化模型

本文利用在约束条件中加入证券多样化选择约束的办法来抵减非系统风险 ,就证券组合投资的选择问题 ,建立了带交易费用的综合考虑收益和风险的多目标规划模型 ,然后通过变换将不可微的多目标规划问题转化为一个多目标线性规划问题 ,最后给出了问题的一个算法和算例     

A mixed R&D projects and securities portfolio selection model

The business environment is full of uncertainty. Allocating the wealth among various asset classes may lower the risk of overall portfolio and increase the potential for more benefit over the long term. In this paper, we propose a mixed single-stage R&D projects and multi-stage securities portfolio selection model. Specifically, we present a bi-objective mixed-integer stochastic programming model. Moreover, we use semi-absolute deviation risk functions to measure the risk of mixed asset portfolio. Based on the idea of moments approximation method via linear programming, we propose a scenario generation approach for the mixed single-stage R&D projects and multi-stage securities portfolio selection problem. The bi-objective mixed-integer stochastic programming problem can be solved by transforming it into a single objective mixed-integer stochastic programming problem. A numerical example is given to illustrate the behavior of the proposed mixed single stage R&D projects and multi-stage securities portfolio selection model.     

整数线性规划投资组合模型的直接搜索算法求解

利用松弛最优邻近解临域整数点搜索法作过滤条件,建立求解整数规划的新方法——直接搜索算法,利用直接搜索算法并借助Matlab软件求解整数线性规划投资组合模型.数值结果表明了模型的建立与提出方法的有效性.     

带有模糊系数的投资组合模型研究

在证券市场,由于各种不确定因素的存在,证券的预期收益率是难以精确估算的。本文采用模糊数来处理不确定性,提出了一种基于模糊收益率的投资组合模型。为度量投资组合的风险,将绝对偏差扩展到模糊情形。通过引入模糊数绝对值的概念和不等关系的两种占优准则,将该模型转化为相应的确定性线性规划问题,投资者可根据自己的主观态度选择参数和投资策略。最后用一个具体例子验证了模型的合理性和有效性。     

模糊环境中带交易费用的投资组合策略问题

由于金融市场是波动的,风险资产的预期收益率由于很多不确定性是很难估计的,本文考虑预期收益率是可能性分布(模糊数),并且在此基础上用模糊数的可能性均值表示投资组合的收益,用模糊数的平均绝对偏差表示风险,考虑了交易费用后,得到投资组合模型,最后给出了数值计算的例子.     

具有熵约束的多阶段均值—绝对偏差模糊投资组合决策

文章运用可能性绝对偏差和比例熵分别度量风险和分散化程度,提出了具有风险控制和线性交易成本的终期财富最大化的多阶段模糊投资组合模型。运用可能理论,将该模型转化为显示的非线性动态优化问题。由于投资过程存在交易成本,上述模型为具有路径依赖性的动态优化问题。文章提出了前向动态规划方法求解。最后, 通过实证研究比较了不同熵的取值投资组合最优投资比例和最终财富的变化。     

一类投资组合选择的线性规划方法研究

如何在摩擦市场下构建最优组合一直是一个非常有意义的问题.人们通常在有效前沿上选择最优的投资组合,但是值得注意的是,如果我们考虑摩擦因素,原本的有效组合将不再有效.探讨如何在无风险借贷利率不同的摩擦市场下构建投资组合模型.为了得到最优策略,我们先利用Karush-Kuhn-Tucker条件给出一类线性规划问题求解方法,然后具体阐述如何将投资决策问题转化为可以求解的线性规划问题,最后给出在无风险借贷利率不同的情况下投资组合的有效边界.     

Probability maximization models for portfolio selection under ambiguity

This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers’ predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model.     

Portfolio optimization with an envelope-based multi-objective evolutionary algorithm

The problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades. Classical mean–variance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance. In the case of linear constraints, the problem can be solved efficiently by parametric quadratic programming (i.e., variants of Markowitz’ critical line algorithm). However, there are many real-world constraints that lead to a non-convex search space, e.g., cardinality constraints which limit the number of different assets in a portfolio, or minimum buy-in thresholds. As a consequence, the efficient approaches for the convex problem can no longer be applied, and new solutions are needed.In this paper, we propose to integrate an active set algorithm optimized for portfolio selection into a multi-objective evolutionary algorithm (MOEA). The idea is to let the MOEA come up with some convex subsets of the set of all feasible portfolios, solve a critical line algorithm for each subset, and then merge the partial solutions to form the solution of the original non-convex problem. We show that the resulting envelope-based MOEA significantly outperforms existing MOEAs.     

Mean-chance model for portfolio selection based on uncertain measure

This paper discusses a portfolio selection problem in which security returns are given by experts’ evaluations instead of historical data. A factor method for evaluating security returns based on experts’ judgment is proposed and a mean-chance model for optimal portfolio selection is developed taking transaction costs and investors’ preference on diversification and investment limitations on certain securities into account. The factor method of evaluation can make good use of experts’ knowledge on the effects of economic environment and the companies’ unique characteristics on security returns and incorporate the contemporary relationship of security returns in the portfolio. The use of chance of portfolio return failing to reach the threshold can help investors easily tell their tolerance toward risk and thus facilitate a decision making. To solve the proposed nonlinear programming problem, a genetic algorithm is provided. To illustrate the application of the proposed method, a numerical example is also presented.     

Interactive multiobjective fuzzy random linear programming: Maximization of possibility and probability

This paper considers multiobjective linear programming problems with fuzzy random variables coefficients. A new decision making model is proposed to maximize both possibility and probability, which is based on possibilistic programming and stochastic programming. An interactive algorithm is constructed to obtain a satisficing solution satisfying at least weak Pareto optimality.     

Genetic algorithms for portfolio selection problems with minimum transaction lots

Conventionally, portfolio selection problems are solved with quadratic or linear programming models. However, the solutions obtained by these methods are in real numbers and difficult to implement because each asset usually has its minimum transaction lot. Methods considering minimum transaction lots were developed based on some linear portfolio optimization models. However, no study has ever investigated the minimum transaction lot problem in portfolio optimization based on Markowitz’ model, which is probably the most well-known and widely used. Based on Markowitz’ model, this study presents three possible models for portfolio selection problems with minimum transaction lots, and devises corresponding genetic algorithms to obtain the solutions. The results of the empirical study show that the portfolios obtained using the proposed algorithms are very close to the efficient frontier, indicating that the proposed method can obtain near optimal and also practically feasible solutions to the portfolio selection problem in an acceptable short time. One model that is based on a fuzzy multi-objective decision-making approach is highly recommended because of its adaptability and simplicity.     

Fuzzy portfolio model with different investor risk attitudes

We propose a fuzzy portfolio model designed for efficient portfolio selection with respect to uncertain or vague returns. Although many researchers have studied the fuzzy portfolio model, no researcher has yet attempted a behavioral analysis of the investor in the fuzzy portfolio model. To address this problem, we examined investor risk attitudes—risk-averse, risk-neutral, or risk-seeking behaviors—to discover an efficient method for fuzzy portfolio selection. In this study, we relied on the advantages of possibilistic mean–standard deviation models that we believed would fit the risk attitudes of investors. Thus, we developed a fuzzy portfolio model that focuses on different investor risk attitudes so that fuzzy portfolio selection for investors who possess different risk attitudes can be achieved more easily. Finally, we presented a numerical example of a portfolio selection problem to illustrate ways to address problems presented by a variety of investor risk attitudes.     

Multiple criteria linear programming model for portfolio selection

The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model. This revised version was published online in June 2006 with corrections to the Cover Date.