含交易费用的证券组合投资模型的满意解

在证券组合投资过程中,忽略交易费用会导致非有效的证券组合投资,本文提出了一个考虑交易费用的证券组合投资的区间数线性规划模型,通过引入区间数线性规划问题中的目标函数优化水平参数λ和约束条件满足水平参数η将目标函数和约束条件均为区间数的区间数线性规划模型转化为确定型的一般线性规划模型,进而求得相应于优化水平λ和满足水平η的满意解.     

区间值模糊线性规划在证券组合投资优化中的应用

针对期望收益率与风险损失率为区间值模糊数的特征,就证券组合投资问题建立了一种区间值模糊线性规划模型,运用一种对区间值模糊数排序的新算法,将模型转化为经典的线性规划问题进行求解,最后通过一个算例说明其有效性和可靠性,为证券组合投资优化问题的解决提供了一种新的方法,对证券组合的理性投资具有重要的指导意义.     

一种基于区间数的证券组合投资模型与求解

提出了区间数的相对左偏度的定义.利用区间数的相对左偏度作为区间数下表达证券风险损失率的一种补充,能合理地反映风险损失率与预期收益率之间的相关关系.建立了一种新的证券组合投资区间数规划模型,将区间数规划模型转化为参数线性规划问题求解,使证券组合投资决策分析更加具有柔性.最后通过实例分析了该模型的应用价值.     

证券组合的模糊规划模型

通过结构元方法定义了一种模糊数排序准则,利用模糊约束将Markowitz投资组舍模型转化为模糊线性规划模型,并利用模糊数来描述证券的期望收益率和风险损失率,建立模糊数模糊证券投资组合模型.最后,利用定义的模糊数排序准则把模糊数规划问题转化为经典的线性规划问题,然后再对该模型进行求解,并通过算例阐述了该方法的有效性.     

一类模糊线性规划模型的模糊最优区间值

讨论一类既有模糊不等式约束又有模糊等式约束的全模糊系数线性规划问题。在给定的模糊隶属度水平下 ,将模型转化为区间数线性规划模型 ,通过确定区间模型的最佳目标函数和最大可行域以及最劣目标函数和最小可行域 ,求出目标函数的模糊最优区间值 ,从而为决策者提供更多的决策信息。最后给出一个数值例子。     

投资组合选择的一种模糊决策方法

针对带有V-型交易费用的半绝对偏差风险函数投资组合问题,利用模糊决策理论,提出了一种新的投资收益目标水平和投资风险目标水平心理满意度的非线性隶属函数,并将满足非线性满意程度的投资组合选择模型转化为线性规划模型,证明了两者的等价性,最后通过实例说明了所建模型的可行性与有效性.     

证券组合投资的多目标区间数线性规划模型

本文提出了证券组合投资的多目标区间数线性规划模型，引入了收益——风险偏好参数和优化水平参数。投资者可以根据对风险的喜好程度和金融市场的客观情况，适当估计这两个参数，从而得到相应情况下的有效投资方案，使投资过程更具柔性，而且更接近于实际情况。     

带有区间型三角模糊数的多目标规划模型算法

给出了模糊多目标线性规划模型的一种有效算法,其中目标函数和约束条件中的系数都是区间型三角模糊数.首先,通过引入区间型三角模糊数的截集,将模糊多目标函数转化成单目标函数.其次,引入用于比较两个三角模糊数的强占优可能性准则,将模型中的模糊约束条件转化为经典不等式组.然后,利用Matlab软件编程求解转化的经典单目标线性规划...     

证券投资组合优化问题的强健性的锥优化方法(英文)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

证券投资组合优化问题的强健性的锥优化方法(英)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

基于区间数贴近度的不确定多属性决策模型

针对只有部分权重信息且属性值以区间数形式给出的多属性决策问题,提出了一种基于区间数贴近度的决策方法.首先讨论了区间数贴近度的定义和性质;然后给出了解决不确定多属性决策问题的一般步骤.并依据传统的逼近理想解的基本思路,以实际评价值与理想解之间的贴近度最大化为目标建立优化模型,从而得到指标权重.进而计算出每个方案与正理想解的相对贴近度,即可得到所有方案的排序结果.方法能充分利用规范化评价的先验信息,评价结果客观可靠,不具有主观随意性.最后通过实例分析验证了该方法的有效性和实用性.     

A nonlinear interval number programming method for uncertain optimization problems

In this paper, a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints. Based on an order relation of interval number, the uncertain objective function is transformed into two deterministic objective functions, in which the robustness of design is considered. Through a modified possibility degree, the uncertain inequality and equality constraints are changed to deterministic inequality constraints. The two objective functions are converted into a single-objective problem through the linear combination method, and the deterministic inequality constraints are treated with the penalty function method. The intergeneration projection genetic algorithm is employed to solve the finally obtained deterministic and non-constraint optimization problem. Two numerical examples are investigated to demonstrate the effectiveness of the present method.     

An interval approach based on expectation optimization for fuzzy random bilevel linear programming problems

This paper considers a class of bilevel linear programming problems in which the coefficients of both objective functions are fuzzy random variables. The main idea of this paper is to introduce the Pareto optimal solution in a multi-objective bilevel programming problem as a solution for a fuzzy random bilevel programming problem. To this end, a stochastic interval bilevel linear programming problem is first introduced in terms of α-cuts of fuzzy random variables. On the basis of an order relation of interval numbers and the expectation optimization model, the stochastic interval bilevel linear programming problem can be transformed into a multi-objective bilevel programming problem which is solved by means of weighted linear combination technique. In order to compare different optimal solutions depending on different cuts, two criterions are given to provide the preferable optimal solutions for the upper and lower level decision makers respectively. Finally, a production planning problem is given to demonstrate the feasibility of the proposed approach.     

A cutting plane method for bilevel linear programming with interval coefficients

This article considers the bilevel linear programming problem with interval coefficients in both objective functions. We propose a cutting plane method to solve such a problem. In order to obtain the best and worst optimal solutions, two types of cutting plane methods are developed based on the fact that the best and worst optimal solutions of this kind of problem occur at extreme points of its constraint region. The main idea of the proposed methods is to solve a sequence of linear programming problems with cutting planes that are successively introduced until the best and worst optimal solutions are found. Finally, we extend the two algorithms proposed to compute the best and worst optimal solutions of the general bilevel linear programming problem with interval coefficients in the objective functions as well as in the constraints.     

An interactive method of tackling uncertainty in interval multiple objective linear programming

Mathematical programming models for decision support must explicitly take account of the treatment of the uncertainty associated with the model coefficients along with multiple and conflicting objective functions. Interval programming just assumes that information about the variation range of some (or all) of the coefficients is available. In this paper, we propose an interactive approach for multiple objective linear programming problems with interval coefficients that deals with the uncertainty in all the coefficients of the model. The presented procedures provide a global view of the solutions in the best and worst case coefficient scenarios and allow performing the search for new solutions according to the achievement rates of the objective functions regarding both the upper and lower bounds. The main goal is to find solutions associated with the interval objective function values that are closer to their corresponding interval ideal solutions. It is also possible to find solutions with non-dominance relations regarding the achievement rates of the upper and lower bounds of the objective functions considering interval coefficients in the whole model.     

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