基于模糊收益率的养老保险基金投资研究

结合中国养老保险基金投资现状,考虑预期收益率是模糊数的情形,利用可能性均值和可能性方差作为投资组合的预期收益率和风险,建立均值-方差组合投资模型.最后,利用lingo软件进行数值分析,表明此模型具有一定的实际应用价值.     

基于模糊收益率的最优投资组合模型

考虑了收益率为模糊数的投资组合问题.在一定置信水平上,用收益率波动差的平方和作为风险的度量,在预期收益率给定时,建立了风险最小化的投资组合模型.投资者可以参考其最优解来减小投资风险.最后给出了一个实例.     

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。     

收益率为模糊数的投资组合问题的讨论

从模糊性的角度考虑选择风险资产投资组合问题 ,对于收益率为模糊数的情形 ,在每一置信水平上 ,以偏离中心值的程度作为风险的度量 ,当预期收益率给定时 ,证明最小风险选择组合的存在性并得到其最优解 ,还给出全局最小风险组合存在的条件及其对应的全局最小风险的算式。     

风险投资决策的模糊分析模型

从不确定性的一个侧面——模糊性的角度研究选择风险资产投资组合的问题，在对模糊预期收益率获取方法研究的基础上，将预期收益率表示为模糊数，对于一定的预期收益率，在每一确信度水平上，以偏离中心值的程度作为风险的度量，对于不允许卖空的情况建立优化决策模型，研究优化决策模型解的性质，并通过数值例子分析了收益一风险之间的关系。得到了风险一收益率曲线。根据这一曲线，投资者可以结合自己的偏好、直观地选择自己的投资方向。     

分式规划模糊投资组合模型的遗传算法求解

将预期收益率表示为模糊数,以E-SV风险测度为基础给出了组合证券投资决策的效用函数,并建立了基于分式规划的模糊投资组合选择模型,考虑到模型求解的复杂性,我们利用遗传算法构造罚函数对模型进行了求解,并通过实例,验证了该模型解法的可行性和有效性.     

基于偏好可能性均值的模糊投资组合模型及实证分析

本文通过客观模糊频数统计法,将证券投资的不确定收益用模糊数来表达,并利用模糊数的可能性均值将模糊收益清晰化,以及采用半绝对偏差函数来度量证券投资的风险,考虑证券换手率约束,构建基于偏好可能性均值—半绝对偏差投资组合模型,并对所建模型进行实证分析.     

考虑背景风险和流动性的模糊投资组合模型

利用投资收益率的二阶矩作为风险度量函数,建立了考虑背景风险和流动性的模糊投资组合模型.在满足预设收益率、换手率可能性均值要求水平以及风险资产的投资比例等约束条件下,使投资收益的二阶矩最小.最后选取中证100指数成分股中部分股票的历史数据进行数值分析,证明了该模型符合“高收益、高风险”的规律,说明该模型适用于实际金融市场.而且使用二阶矩代替方差作为风险度量函数,克服了方差计算复杂的缺陷,简化了模糊投资组合求解问题.     

模糊预期收益率下风险损失率的左偏差度量

为在模糊预期收益率下度量证券的风险损失率 ,引入模糊数的左偏差的定义 ,给出模糊数的左偏差的一个性质和三角型模糊数的左偏差的计算公式。利用模糊预期收益率的左偏差定义了相应的风险损失率 ,这种定义能合理地反映证券的风险损失率与预期收益率之间的对应关系 ,并将这种关系用一个模糊集来表达 ,最给出一个应用示例     

考虑投资者风险态度的随机模糊投资组合模型及实证

考虑投资者面临证券市场随机和模糊的双重不确定性,把证券收益率视为随机模糊变量。在前景理论下考虑投资者的风险态度,建立不同的随机模糊收益率、期望收益隶属度函数和目标权重,构建考虑投资者风险态度的随机模糊投资组合模型。采用实证方法把市场分为下降和上升两个阶段,研究不同风险态度投资者的投资组合差异及模型表现。结果表明:投资者的风险态度会影响投资组合的结构;考虑投资者风险态度的随机模糊投资组合模型,能够满足不同风险态度投资者对投资收益和风险的差异需求,且在实际投资决策中具有可行性。     

On the possibilistic mean value and variance of multiplication of fuzzy numbers

In this paper, we introduce the definitions of the possibilistic mean, variance and covariance of multiplication of fuzzy numbers, and show some properties of these definitions. Then, we apply these definitions to build the possibilistic models of portfolio selection under the situations involving uncertainty over the time horizon, by considering the portfolio selection problem from the point of view of possibilistic analysis. Moreover, numerical experiments with real market data indicate that our approach results in better portfolio performance.     

An extension of Sharpe's single-index model: portfolio selection with expert betas

This paper presents an approach to the portfolio selection problem based on Sharpe's single-index model and on Fuzzy Sets Theory. In this sense, expert estimations about future Betas of each financial asset have been included in the portfolio selection model denoted as ‘Expert Betas’ and modelled as trapezoidal fuzzy numbers. Value, ambiguity and fuzziness are three basic concepts involved in the model which provide enough information about fuzzy numbers representing ‘Expert Betas’ and that are simple to handle. In order to select an optimal portfolio, a Goal Programming model has been proposed including imprecise investor's aspirations concerning asset's proportions of both, high-and low-risk assets. Semantics of these goals are based on the fuzzy membership of a goal satisfaction set. To illustrate the proposed model a real portfolio selection problem is presented.     

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.     

Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.     

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.     

Fuzzy portfolio selection model with real features and different decision behaviors

In the ever changing financial markets, investor’s decision behaviors may change from time to time. In this paper, we consider the effect of investor’s different decision behaviors on portfolio selection in fuzzy environment. We present a possibilistic mean-semivariance model for fuzzy portfolio selection by considering some real investment features including proportional transaction cost, fixed transaction cost, cardinality constraint, investment threshold constraints, decision dependency constraints and minimum transaction lots. To describe investor’s different decision behaviors, we characterize the return rates on securities by LR fuzzy numbers with different shape parameters in the left- and right-hand reference functions. Then, we design a novel hybrid differential evolution algorithm to solve the proposed model. Finally, we provide a numerical example to illustrate the application of our model and the effectiveness of the designed algorithm.     

基于EEMD与模糊回归的投资组合选择模型及实证

随着模糊理论的不断发展与其在证券市场的广泛应用,越来越多的学者关注到参数模糊化对投资组合优化具有重要作用。本文利用集合经验模态分解(EEMD)和模糊线性回归相结合的预测方法,构建了基于对称三角模糊数的投资组合模型。并将提出的模型与集合经验模态分解和普通最小二乘结合的方法、单一模糊线性回归方法进行了对比分析,结果表明基于集合经验模态分解和模糊线性回归建立的投资组合模型最优,这对构建最优投资组合具有参考意义。     

基于模糊决策的投资组合优化

基于模糊决策理论研究了带有成比例交易费用的证券投资组合优化问题. 首先,基于半绝对偏差风险函数和极大极小原则提出了一种新的风险函数--极大极小半绝对偏差风险函数;然后, 引入一种非线性隶属函数更加形象地描述了投资者对投资收益和投资风险的满意程度;在此基础上, 进一步提出了非线性满意程度的模糊决策投资组合选择模型;最后, 针对提出的模型,利用中国证券市场的真实数据给出了数值算例.     

Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature

Since the pioneering work of Harry Markowitz, mean–variance portfolio selection model has been widely used in both theoretical and empirical studies, which maximizes the investment return under certain risk level or minimizes the investment risk under certain return level. In this paper, we review several variations or generalizations that substantially improve the performance of Markowitz’s mean–variance model, including dynamic portfolio optimization, portfolio optimization with practical factors, robust portfolio optimization and fuzzy portfolio optimization. The review provides a useful reference to handle portfolio selection problems for both researchers and practitioners. Some summaries about the current studies and future research directions are presented at the end of this paper.