多阶段资产组合选择均值-VaR模型和均值-方差模型的比较

本文建立了多阶段情形下的均值-方差模型和均值-VaR模型,并比较了两种模型的不同性质,给出了两种模型下的最小方差组合性质和在收益率的均值-标准差坐标下,不同的风险度量方法产生的不同的有效边缘以及VaR模型置信度趋于1时的极限性质,最后给出了分析的数值例子.     

参数不确定性和效用最大化下的动态投资组合选择

标准投资组合选择理论假设投资者准确地知道与资产收益率相关的各种参数(例如均值和方差),忽视了参数不确定性引致的估计风险给投资决策带来的影响.本文研究引入参数不确定和学习时的连续时间动态投资组合选择问题,使用鞅方法求导出了具有CRRA型效用函数的投资者的最优投资策略的显式表达式.在此基础上,我们结合中国证券市场中的实际数据深入分析了参数不确定性以及投资者初始信念对最优投资策略的影响.     

均值-方差模型具有一般不确定性下的最优资产组合选择

引入以记忆系数和无差异系数表征的随机变量测度均值-方差模型的一般不确定性特征,反映投资者的模型信任程度,研究均值-方差模型具有一般不确定性下的最优资产组合选择问题。基于资本市场线理论,构建最优资产组合选择是模型信任程度和基于均值-方差模型的传统资产组合选择的线性函数;基于记忆系数和无差异系数的不同组合,运用基于事例推理的方法求解二次效用投资者的最优模型信任程度,获得均值-方差模型具有一般不确定性下的最优资产组合,并以上证综指1997年1月-2014年8月的月度收益数据形成两个研究样本予以实证比较研究。结果表明,较大风险规避投资者,在较大记忆系数和较小无差异系数下,其模型信任程度调整较快、资产组合调整幅度大,表现出可获得性和代表性行为偏差,通常采取积极资产组合策略;反之,其模型信任程度调整渐进、资产组合调整幅度小,表现出锚定性和保守性行为偏差,通常采取消极资产组合策略;模型一般不确定性对最优资产组合选择的影响强于股票市场记忆性的影响。研究体现了投资者的有限理性,将传统的资产组合选择问题延伸至行为金融学领域。     

投资组合均值-方差模型和极小极大模型的实证比较

本文针对传统的Markowitz均值-方差(MV)模型和Young(1998)提出的极小极大(Minimax)模型进行了实证比较研究。我们将2001年上证30指数的实际数据分成两部分,一部分作为样本数据进行优化组合分析,另一部分作为非样本数据进行模拟投资,检验绩效。结果发现:在同样的样本数据下,由两种模型的解描绘的风险-收益率有效前沿图非常相似;将两组模型的最优解分别进行模拟投资,Minimax模型的结果明显优于MV模型。本文的实证结果检验了Minimax模型的理论结论,表明其在实际投资中具有良好的可操作性和实用价值。     

动态均值-方差资产组合的有效性:时变风险容忍度视角

尽管均值-方差模型在静态资产组合优化过程中得到广泛运用并证明是有效的,但在动态情景下,均值-方差模型运用于动态资产组合优化过程中的有效性问题引起人们的质疑：一是常风险规避系数的设定不符合事实;二是投资者偏好设定不符合动态情景下的主流效用函数族。鉴于此,本文假设投资者风险容忍度是资产组合投资期与投资者期望收益率的函数,研究动态均值-方差资产组合的有效性问题。基于均值-方差分析框架构建时变风险容忍度下的动态资产组合模型;运用伊藤定理和拉格朗日乘子法获得最优资产组合封闭解;基于二次效用偏好下的动态资产组合,从资产组合策略、夏普率、确定性等价收益率和有效前沿等视角验证动态均值-方差资产组合策略和业绩,并予以实证。结果表明：动态均值-方差资产组合不但具有同等业绩而且体现了其灵活性和风险对冲价值;尽管动态均值-方差资产组合表现出高杠杆性,但其确定性等价收益率较高,且随投资期的增加呈现倒U型趋势;动态均值-方差资产组合的投资期效应显著,强于投资者期望收益率。研究指出,时变风险容忍度下的动态均值-方差资产组合管理和优化策略有效,但在短投资期（低于12个月）和（或）低期望收益率下并不适用。研究不但拓展了均值-方差模型在动态情境下的应用,而且体现了投资者源于心理和（或）其财富变化的投资行为调整。     

变动均值和方差资产配置模型的应用研究

本文在均值-方差模型的基础上,以改善估计误差为主线,选取了10种变动均值-方差的资产配置模型,以等权重策略为基准,运用了确定性等价收益和Alpha值为判断准则,同时考虑了允许卖空限制和非允许卖空的情况,实证研究结果表明：虽然在资本市场中配置模型并不能显著战胜等权重策略,但随着投资范围的扩大,模型开始显现配置效果,尤其在Alpha准则下,变动均值-方差资产配置显著。同时本文还将实证结果和目前我国投资者的实际资产配置情况进行了比较,发现了现实配置结构中的不合理之处,并提出了相应的改善建议。最后对4类常用资产进行了模拟研究,其结果也进一步证实了本文的结论。     

基于均值-AS模型的资产配置

AS指标是诺贝尔经济学奖得主Aumann与其合作者Serrano近期基于不确定条件下的选择理论提出的新的风险度量指标,具有诸多优点,被学者们广泛关注.本文基于均值-AS模型研究了正态分布和一般分布下的资产配置问题.在正态分布下,得到了组合边界的解析式,深入探讨了组合边界的特征.在一般分布下,将AS指标的矩估计式嵌入均值-AS模型,实现了风险估计与投资组合优化同步进行.在较弱的条件下,证明了均值-AS模型是凸优化问题,可基于迭代思想设计算法得到模型的数值解.蒙特卡洛模拟结果表明该模型和算法准确有效.最后,基于中国A股市场数据给出了实例分析.     

参数不确定性对投资者最优资产组合的影响：基于中国的实证

现代金融学主要目标是给出具有科学依据的投资建议。这一任务对于投资期限较短的投资者已完成,但对面临时变性投资机会的长期投资者,金融学家还不能给出高精度的投资建议。文章考虑投资者自身预测力存在估计误差的感知风险(参数不确定性)对投资者最优资产组合选择问题的影响。运用我国资本市场数据的实证研究表明:忽略参数不确定性对资产组合选择问题的影响将会误导投资者配置过多的风险资产。     

基于VaR的金融资产配置模型

本文根据均值-方差模型的框架,建立了用VaR代替方差或标准差作为风险的测量指标时的均值-VaR模型,同时使用等VaR线分析了两种模型的内在联系。作为模型的扩展本文还分别考虑了存在无风险资产,负债和非正态分布时的情形。此外讨论了均值-VaR模型有效边界的一些性质。     

考虑均值-方差风险量化的VMI供应链协调模型

针对众多企业风险规避的特性，构建了产出不确定环境下的供应链最优投入决策模型，并采用均值-方差模型来量化决策者的风险规避态度，讨论了风险规避的集成供应链和风险规避的VMI供应商在不同风险承受能力下的最优投入决策.研究表明，最优投入决策与其风险承受能力密切相关，且在给定风险承受能力下，决策者具有两种投入量备选方案.当选择低投入量所需承担的缺货损失低于选择高投入量所需承担的库存积压损失时，决策者将选择较低的投入量；否则，决策者将选择较高的投入量.本文进一步引入两种不同类型的契约来协调VMI供应链：成本共担-批发价折扣联合契约和期权契约.研究表明，这两种契约在一定条件下均能够协调VMI供应链，但这两种契约实现供应链帕累托改进的效果受到决策者风险承受能力的影响.     

A novel portfolio selection model in a hybrid uncertain environment

The future returns of each securities cannot be correctly reflected by the securities data in the past, therefore the statistical techniques and the experts’ judgement and experience are combined together to estimate the security returns in the future. In this paper, the returns of each securities are assumed to be fuzzy random variables, then following the ideas of mean variance model a new portfolio selection model in a hybrid uncertain environment is proposed. Moreover, the λ-mean variance efficient frontiers and λ-mean variance efficient portfolios are defined, and the properties of λ-mean variance efficient portfolios located on different λ-mean variance efficient frontiers are discussed. Finally, a numerical example is presented to illustrate the proposed portfolio selection model. On the basis of the results, we can conclude that the proposed model can provide the more flexible results.     

A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation

We consider a robust optimization model of determining a joint optimal bundle of price and order quantity for a retailer in a two-stage supply chain under uncertainty of parameters in demand and purchase cost functions. Demand is modeled as a decreasing power function of product price, and unit purchase cost is modeled as a decreasing power function of order quantity and demand. While the general form of the power functions are given, it is assumed that parameters defining the two power functions involve a certain degree of uncertainty and their possible values can be characterized by ellipsoids. We show that the robust optimization problem can be transformed into an equivalent convex optimization which can be solved efficiently and effectively using interior-point methods. In addition, we propose a practical implementation of the model, where the stochastic characteristics of parameters are obtained from regression analysis on past sales and production data, and ellipsoidal representations of the parameter uncertainties are obtained based on a combined use of genetic algorithm and Monte Carlo simulation. An illustrative example is provided to demonstrate the model and its implementation.     

A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation

We consider a robust optimization model of determining a joint optimal bundle of price and order quantity for a retailer in a two-stage supply chain under uncertainty of parameters in demand and purchase cost functions. Demand is modeled as a decreasing power function of product price, and unit purchase cost is modeled as a decreasing power function of order quantity and demand. While the general form of the power functions are given, it is assumed that parameters defining the two power functions involve a certain degree of uncertainty and their possible values can be characterized by ellipsoids. We show that the robust optimization problem can be transformed into an equivalent convex optimization which can be solved efficiently and effectively using interior-point methods. In addition, we propose a practical implementation of the model, where the stochastic characteristics of parameters are obtained from regression analysis on past sales and production data, and ellipsoidal representations of the parameter uncertainties are obtained based on a combined use of genetic algorithm and Monte Carlo simulation. An illustrative example is provided to demonstrate the model and its implementation.     

后备技术不确定下资源耗竭动态优化模型研究

不确定性是资源耗竭理论的一个重要研究方向,资源替代研究中经常涉及技术不确定问题.在技术出现时间不确定问题描述的基础上,考虑资源开采成本与开采量相关以及有存货情形,利用动态规划思想处理了技术出现时间不确定,构建了动态优化模型,得到相应地HJB方程和最优开采路径.研究结果表明:确定性情形是不确定性的特例;在早期开采阶段,资源开采速度随着替代技术出现可能性提高而加快,开采了一段时间后,资源的开采速度随着替代技术出现可能性提高而减慢;关系转折时间点取决于资源初始储量,初始储量越大,该时间点越往后延长.     

An interactive three-stage model for mutual funds portfolio selection

The aim of this work is to be a useful instrument for helping finance practitioners on the selection of suitable mutual fund portfolios. The portfolio selection problem is characterized by imprecision and/or vagueness inherent in the required data and more generally, in the context where investors have to make decisions. In order to mitigate these problems, a three stage model has been proposed based on a multi-index model and considering several market scenarios described in an imprecise way by an expert. The proposed fuzzy model allows the Decision Maker to select, by means of an outranking method, a suitable portfolio taking into account the uncertainty related to the market scenarios and the imprecision and/or vagueness associated with the model data.     

Overviewing the transition of Markowitz bi-criterion portfolio selection to tri-criterion portfolio selection

Over 60 years ago, Markowitz introduced the mean-variance efficient frontier to finance. While mean-variance is still the predominant model in portfolio selection, it has endured many criticisms. One serious one is that it does not allow for additional criteria. The difficulty is that the efficient frontier becomes a surface. With it now possible to compute such a surface, we provide an overview on how Markowitz’s risk-return (bi-criterion) portfolio selection can be extended to tri-criterion portfolio selection. With a focus on the geometry of the extension, many graphs are used to illustrate.     

资本结构作用下市场投资组合轨迹的研究

根据企业理财中投融资决策的互动机理 ,将资本结构与投资组合优化结合起来 ,在证券组合模型基础上 ,引入资本结构这一重要因素 ,研究了资本结构作用下市场投资组合点的轨迹 ,从而得出任一资本结构下所对应的市场投资组合     

Surgical scheduling under uncertainty by approximate dynamic programming

Surgical scheduling consists of selecting surgeries to be performed within a day, while jointly assigning operating rooms, starting times and the required resources. Patients can be elective or emergency/urgent. The scheduling of surgeries in an operating theatre with common resources to emergency or urgent and elective cases is highly subject to uncertainties not only on the duration of an intervention but mainly on the arrival of emergency or urgent cases. At the beginning of the day we are given a candidate set of elective surgeries with and an expected duration and a time window the surgery must start, but the expected duration and the time window of an emergency or urgent case become known when the surgery arrives. The day is divided into decision stages. Due to the dynamic nature of the problem, at the beginning of each stage the planner can make decisions taking into account the new information available. Decisions can be to schedule arriving surgeries, and to reschedule or cancel surgeries not started yet. The objective is to minimize the total expected cost composed of terms related to refusing arriving surgeries, to canceling scheduled surgeries, and to starting surgeries out of their time window. We address the problem with an approximate dynamic programming approach embedding an integer programming formulation to support decision making. We propose a dynamic model and an approximate policy iteration algorithm making use of basis functions to capture the impact of decisions to the future stages. Computational experiments have shown with statistical significance that the proposed algorithm outperforms a lookahead reoptimization approach.     

A fuzzy set approach for R&D portfolio selection using a real options valuation model

Making R&D portfolio decision is difficult, because long lead times of R&D and market and technology dynamics lead to unavailable and unreliable collected data for portfolio management. The objective of this research is to develop a fuzzy R&D portfolio selection model to hedge against the R&D uncertainty. Fuzzy set theory is applied to model uncertain and flexible project information. Since traditional project valuation methods often underestimate the risky project, a fuzzy compound-options model is used to evaluate the value of each R&D project. The R&D portfolio selection problem is formulated as a fuzzy zero–one integer programming model that can handle both uncertain and flexible parameters to determine the optimal project portfolio. A new transformation method based on qualitative possibility theory is developed to convert the fuzzy portfolio selection model into a crisp mathematical model from the risk-averse perspective. The transformed model can be solved by an optimization technique. An example is used to illustrate the proposed approach. We conclude that the proposed approach can assist decision makers in selecting suitable R&D portfolios, while there is a lack of reliable project information.