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。     

考虑投资者异质信念和目标优先级的投资组合问题研究

考虑证券市场的模糊不确定性及投资者的模糊决策特征,以资产收益、下方风险及流动性为模糊投资目标,构建考虑投资者异质信念和目标优先级的多目标投资组合模型。进一步,以我国主板、中小板和创业板市场为背景,采用CPT-TOPSIS交互式算法进行实证分析。研究发现:乐观、理性和悲观投资者权衡收益、风险和流动性目标时偏好的优先顺序不同,导致资产配置结构、最优决策和绩效表现存在差别。结果表明模糊多目标模型能够满足不同投资者权衡多目标的差异化投资需求,取得优于基准随机投资组合的投资效果,可作为投资者投资决策的参考依据。     

具有投资限制的风险资产模糊随机投资组合模型

研究了模糊随机环境下风险资产投资组合选择问题.利用模糊随机变量刻画风险资产的收益率,建立了具有投资限制的风险资产投资组合选择的一般模糊随机均值-方差模型,该模型包括了是否允许卖空及具有投资比例下界约束的情况.在此基础上,提出了具有梯形模糊随机收益率的具体投资组合优化模型,这些模型能够转化为二次规划问题求解.最后,利用上证50指数中的9种股票对模型进行了实证分析,结果表明模型能够有效分散非系统性风险.     

基于背景风险和弹性增量的模糊投资组合研究

在金融市场中,投资者需要通过构建投资组合分散非系统风险,也需要考虑由收入、支出、健康状况等个人因素构成的背景风险.另外,在同一个投资组合中,不同的风险存量加上相同的弹性增量以后,投资者的满意度也不同.同时,证券市场中存在大量的模糊现象,模糊性比随机性更能刻画其不确定性特征.因此,提出了一个以投资者满意度为目标,包含背景风险、弹性增量等因素的模糊投资组合模型.最后,选取沪深证券市场数据分析了背景风险方差对投资组合的收益、方差和投资者满意度的影响.结果发现:背景风险的方差与投资组合的收益和投资者的满意度负相关,与投资组合的方差正相关,而且,在不同弹性存量的基础上,相同弹性增量的投资者满意度也是不同的.     

基于最大期望满意度与背景风险的模糊投资组合模型研究

模糊投资组合是不确定性理论研究的重要领域.然而,由于人的理性局限性,投资者在决策的过程中,可能不是追求理性的效用最大化,而是追求心理满意度的最大化;在金融市场中,投资者不仅面临市场风险,也需要承担由自身因素产生的背景风险.因此,提出了一个考虑背景风险等因素的最大期望满意度模型,该模型的目标是最大化投资组合收益与最小收益证券的差值;最后,以上海证券交易所180指数的十支证券构成的的投资组合为例,分析了此模型在分散投资风险与增加满意度方面的有效性.     

摩擦市场条件下的双目标投资组合模型模糊优化

首先建立了摩擦市场条件下基于收益率分布偏度水平的双目标投资组合模型.在此基础上,将模糊集合的概念引入到该模型中,用模糊数学中的线性隶属函数处理了其中的风险目标和收益目标,建立了摩擦市场条件下基于收益率分布偏度水平的模糊型双目标投资组合模型.然后,针对该模型进行了新型遗传算法设计(动态遗传算法).最后用一个具体的算例给出了该模型的一个实例最优解,体现了多样化投资分散风险的组合投资原理.     

随机模糊的等比例-最小方差投资组合优化研究

Markowitz的均值-方差模型在投资组合优化中得到了广泛的运用和拓展,其中多数拓展模型仅局限于对随机投资组合或模糊投资组合的研究,而忽略了实际问题同时包含了随机信息和模糊信息两个方面。本文首先定义随机模糊变量的方差用以度量投资组合的风险,提出具有阀值约束的最小方差随机模糊投资组合模型,基于随机模糊理论,将该模型转化为具有线性等式和不等式约束的凸二次规划问题。为了提高上述模型的有效性,本文以投资者期望效用最大化为压缩目标对投资组合权重进行压缩,构建等比例-最小方差混合的随机模糊投资组合模型,并求解该模型的最优解。最后,运用滚动实际数据的方法,比较上述两个模型的夏普比率以验证其有效性。     

基于旋转算法的随机模糊均值-方差投资组合优化

Markowitz首先采用方差度量风险，并应用于投资组合优化中，大多数的均值方差模型仅对随机投资组合优化或模糊投资组合优化进行研究，然而，实际投资组合优化问题既包含随机信息也包含模糊信息。本文首先定义随机模糊变量的方差，并用其度量风险，提出了具有交易成本、借贷约束和阀值约束的均值-方差随机模糊投资组合优化模型。基于随机模糊理论，将上述模型转化为具有线性等式和线性不等式约束的凸二次规划问题，并得到其KKT条件。本文还提出改进的旋转算法求解上述模型，该算法消掉KKT条件中部分变量，减少计算量。最后，采用中国证券市场的实际数据进行样本内分析和样本外分析，验证了上述模型和算法的有效性。     

模糊随机环境下带个人偏好的投资组合决策模型

在现实的证券市场中,存在许多混合不确定性因素对证券的收益率产生影响.本文的目的是建立糊随机环境下带个人偏好的投资组合决策模型.在模糊随机环境下将证券的收益率视为模糊随机变量,同时考虑到投资者的偏好,提出入均值和投资者的风险曲线的概念,他们分别反映投资组合的收益和风险.文中给出新的入均值有效投资组合和入均值有效前沿的概念,探讨新的投资组合的收益率与偏好参数入的关系;最后本文采用混合智能算法进行实例分析,结果表明本文所提模型是可行性的.     

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.     

Portfolio rebalancing model with transaction costs based on fuzzy decision theory

The fuzzy set is one of the powerful tools used to describe an uncertain environment. As well as quantifying any potential return and risk, portfolio liquidity is taken into account and a linear programming model for portfolio rebalancing with transaction costs is proposed. The level of return that an investor might aspire to, the risk and the liquidity of portfolio are vague in an uncertain financial environment. Considering them as fuzzy numbers, we propose a portfolio rebalancing model with transaction costs based on fuzzy decision theory. An example is given to illustrate the behavior of the proposed model using real data from the Shanghai Stock Exchange.     

Exact and heuristic procedures for solving the fuzzy portfolio selection problem

We propose a fuzzy model for the portfolio selection problem which takes into account the vagueness of the investor’s preferences regarding the assumed risk. We also describe an exact method for solving it as well as a hybrid meta-heuristic procedure which is more adequate for medium and large-sized problems or in cases in which a quick solution is needed. As an application, we solve several problems based on data from the IBEX35 index and the Spanish Stock Exchange Interconnection System.     

二阶随机占优约束下考虑偏度的投资组合模型

在DentchevaRuszczynski(2006)模型的基础上,考虑偏度对构建投资组合的影响,建立了二阶随机占优约束下最大化组合收益率偏度的投资组合优化模型,并应用分段线性近似方法将模型转化为一个非线性混合整数规划问题.利用中国股票市场的历史数据对所建模型进行了实证分析,结果表明,所建新模型比均值-方差-偏度模型和市场指数具有更稳健的表现.     

An expected regret minimization portfolio selection model

Fuzzy portfolio selection has been widely studied within the framework of the credibility theory. However, all existing models provide only concentrated investment solutions, which contradicts the risk diversification concept in the classical portfolio selection theory. In this paper, we propose an expected regret minimization model, which minimizes the expected value of the distance between the maximum return and the obtained return associated with each portfolio. We prove that our model is advantageous for obtaining distributive investment and reducing investor regret. The effectiveness of the model is demonstrated by using an example of a portfolio selection problem comprising ten securities in the Shanghai Stock Exchange 180 Index.     

On the effectiveness of scenario generation techniques in single-period portfolio optimization

In single-period portfolio selection problems the expected value of both the risk measure and the portfolio return have to be estimated. Historical data realizations, used as equally probable scenarios, are frequently used to this aim. Several other parametric and non-parametric methods can be applied. When dealing with scenario generation techniques practitioners are mainly concerned on how reliable and effective such methods are when embedded into portfolio selection models. In this paper we survey different techniques to generate scenarios for the rates of return. We also compare the techniques by providing in-sample and out-of-sample analysis of the portfolios obtained by using these techniques to generate the rates of return. Evidence on the computational burden required by the different techniques is also provided. As reference model we use the Worst Conditional Expectation model with transaction costs. Extensive computational results based on different historical data sets from London Stock Exchange Market (FTSE) are presented and some interesting financial conclusions are drawn.     

基于自组织映射和模糊隶属度的财务危机预警研究

良好的财务危机预警模型能够有效监控企业运营情况,避免企业倒闭或被重组的悲剧发生。本文结合自组织映射模型和模糊C均值的模糊隶属度,构造模糊自组织映射模型,并应用到财务危机预警中。该模型将模糊隶属度带入到学习率函数中,在计算过程中自动更新获胜节点邻域范围,并在迭代过程中采用批学习算法,提高预测精度、稳定输出结果。对沪深两市上市公司的财务指标进行实证研究,通过与传统预警模型对比,得出模糊自组织映射模型在财务危机预警方面具有更优越的预测性能。     

A stochastic programming approach to multicriteria portfolio optimization

We study a stochastic programming approach to multicriteria multi-period portfolio optimization problem. We use a Single Index Model to estimate the returns of stocks from a market-representative index and a random walk model to generate scenarios on the possible values of the index return. We consider expected return, Conditional Value at Risk and liquidity as our criteria. With stocks from Istanbul Stock Exchange, we make computational studies for the two and three-criteria cases. We demonstrate the tradeoffs between criteria and show that treating these criteria simultaneously yields meaningful efficient solutions. We provide insights based on our experiments.     

基于最速曲线的投资组合调整方法

均值方差模型自1952年被提出以来在单期投资组合优化理论与实践中一直扮演着十分重要的角色。然而因为资金具有时间价值,所以投资者总是希望能够尽快实现他们的投资目标。鉴于此,本文利用数学中著名的最速曲线提出了一种新的投资组合调整方法并探讨其求解步骤。该方法在建模过程中考虑了投资活动中普遍存在的时间效应和处置效应两种现象。德国股票市场和中国股票市场中的实证结果不仅证实了投资组合调整的必要性,而且说明了新方法的实用性和有效性。     

Selecting Portfolios with Fixed Costs and Minimum Transaction Lots

The original Markowitz model of portfolio selection has received a widespread theoretical acceptance and it has been the basis for various portfolio selection techniques. Nevertheless, this normative model has found relatively little application in practice when some additional features, such as fixed costs and minimum transaction lots, are relevant in the portfolio selection problem. In this paper different mixed-integer linear programming models dealing with fixed costs and possibly minimum lots are introduced. Due to the high computational complexity of the models, heuristic procedures, based on the construction and optimal solution of mixed integer subproblems, are proposed. Computational results obtained using data from the Milan Stock Exchange show how the proposed heuristics yield very good solutions in a short computational time and make possible some interesting financial conclusions on the impact of fixed costs and minimum lots on portfolio composition.