改进区间可接受度的证券投资组合区间二次规划模型

本文首先基于Markowitz的经典均值方差模型，针对不确定环境下的投资组合问题，把证券的收益率、风险损失率和流动性用区间数描述，建立了一种新的含交易成本的证券投资组合区间二次规划模型。其次，为求解该模型，提出了改进的区间可接受度确定性转换方法，通过引入优化水平α与可接受水平η将不确定二次规划转化为确定型规划。最后，通过数值实验将提出的方法与传统方法进行比较，结果表明本文所提出的方法与模型具有相对较好的可行性与实用性。     

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.     

具有最小交易量限制的多阶段均值-半方差投资组合优化

考虑交易成本,借款约束和阈值约束,文章提出了具有最小交易量限制的多阶段均值-半方差投资组合模型。该模型是具有路径依赖性的混合整数动态优化问题,还是NP完全问题。文章提出了前向动态规划方法求解。最后,通过一个算例比较不同风险约束下的最优投资策略,从而验证模型和算法的有效性。     

Integrated supply,production and distribution scheduling under disruption risks

This paper presents a bi-objective stochastic mixed integer programming approach for a joint selection of suppliers and scheduling of production and distribution in a multi-echelon supply chain subject to local and regional disruption risks. Two conflicting problem objectives are minimization of cost and maximization of service level. The three shipping methods are considered for distribution of products: batch shipping with a single shipment of different customer orders, batch shipping with multiple shipments of different customer orders and individual shipping of each customer order immediately after its completion. The stochastic combinatorial optimization problem is formulated as a time-indexed mixed integer program with the weighted-sum aggregation of the two objective functions. The supply portfolio is determined by binary selection and fractional allocation variables while time-indexed assignment variables determine the production and distribution schedules. The problem formulation incorporates supply–production, production–distribution and supply–distribution coordinating constraints to efficiently coordinate supply, production and distribution schedules. Numerical examples modelled after an electronics supply chain and computational results are presented and some managerial insights are reported. The findings indicate that for all shipping methods, the service-oriented supply portfolio is more diversified than the cost-oriented portfolio and the more cost-oriented decision-making, the more delayed the expected supply, production and distribution schedules.     

摩擦市场上允许买空卖空的投资组合问题

证券交易市场上存在着诸如交易费用、税收等摩擦.投资者在交易过程中,不可避免地要受到市场摩擦的影响.本文以投资者所获取的最大投资效用为目标函数,建立了摩擦市场上最优投资组合问题的数学模型;同时对于之前解决此类问题的很多文章中“证券市场不允许买空卖空风险资产和借贷无风险资产”的假设条件做了扩展,得到一个摩擦市场上适用于“允许买空卖空或借贷”的证券投资组合的二次规划模型.     

资源约束下可打断项目组合选择模型研究

首先,本文在已有可打断项目组合选择模型的基础上,引入了消耗性资源和可更新资源约束,构建了一个更符合实际的新模型;其次,为了达到模型简化的目的,本文给出了资金约束的现值表示,并给出了理论证明;最后,利用GAMS对模型进行了算例分析。数值实验结果表明：1）资源约束下的项目打断有时可以给企业带来积极效益,这有别于已有的研究;2）在考虑资源约束的情况下,资源消耗少且同时收益高的项目应优先执行;3）当资源的供给量较少时,资源约束是决定项目选择的关键因素。此外,通过企业实际的案例对数值实验结果进行了验证。     

基于Expectile回归的均值-ES组合投资决策

为解决均值-ES（Expected Shortfall）组合投资决策中的计算困难，通过理论证明将其转化为一个Expectile回归问题，进而给出其Expectile回归求解新方法。该方法具有两个方面的优势：第一，Expectile回归的目标函数为二次损失函数，具有连续、光滑等特性，其优化与计算过程简单易行，且具有很好的可扩展性；第二，优化Expectile回归目标函数得到Expectile，利用Expectile与ES之间对应关系，能够准确地得到最优组合投资的ES风险值。选取沪深300指数中具有行业代表性的5支股票进行实证研究，将基于Expectile回归的均值-ES模型与均值-VaR模型、均值-方差模型进行对比，发现前者能够很好地分散组合投资尾部风险大小，显著提高组合投资绩效。     

Application of the Fuzzy Weighted Average in Strategic Portfolio Management*

We propose a systematic approach that incorporates fuzzy set theory in conjunction with portfolio matrices to assist managers in reaching a better understanding of the overall competitiveness of their business portfolios. Integer linear programming is also accommodated in the proposed integrated approach to help select strategic plans by using the results derived from the previous portfolio analysis and other financial data. The proposed integrated approach is designed from a strategy‐oriented perspective for portfolio management at the corporate level. It has the advantage of dealing with the uncertainty problem of decision makers in doing evaluation, providing a technique that presents the diversity of confidence and optimism levels of decision makers. Furthermore, integer linear programming is used because it offers an effective quantitative method for managers to allocate constrained resources optimally among proposed strategies. An illustration from a real‐world situation demonstrates the integrated approach. Although a particular portfolio matrix model has been adopted in our research, the procedure proposed here can be modified to incorporate other portfolio matrices.     

PORTFOLIO MODELING IN MULTIPLE-CRITERIA SITUATIONS UNDER UNCERTAINTY

There have been many models for portfolio selection, but most do not explicitly include uncertainty and multiple objectives. This paper presents an approach that includes these aspects using a form of stochastic integer programming with recourse. The method involves the use of a time-based decision tree structure called a “project tree.” Using this basic format, an illustrative six-project example is presented and analyzed. Various forms of objectives are discussed, ranging from the maximization of expected portfolio value to the maximization of the minimum weighted portfolio deviation from two goals. In each case, formulated numerical problems are given, and the solutions derived are presented. The approach is shown to be very flexible and capable of handling a variety of situations and objectives.     

限制性卖空的均值-半绝对偏差投资组合模型及其旋转算法研究

本文提出了限制性卖空的均值-半绝对偏差投资组合模型,通过变量替换将该模型转变为一般线性规划问题,从而运用线性规划的旋转算法进行求解。最后,文章以一个具体的算例验证了该算法的有效性,并证明将限制性卖空引入到投资组合中,有助于增强市场效率,降低市场风险。     

Linear programming techniques in R & D project planning

In a multi-project industrial R & D organization the selection of projects with potentially good payoffs has to be fitted in with the planning of on-going projects as they compete for the same expert staff, laboratory equipment, pilot plant rigs and other facilities and resources. A linear programming approach to this planning problem takes account of any flexibility possible in allocating resources to projects, and in their timing in finding the ‘best’ plan. This is the one which maximises the potential payoff for the whole ‘portfolio’ of projects and makes the most efficient use of the available resources. The principles of the formulation of such LP models and the interpretation of the results produced in terms of practical planning are discussed.     

Portfolio optimization: New capabilities and future methods

Summary  This paper addresses the problem of portfolio selection in finance. In many cases, currently available software to compute the efficient frontier runs into difficulty in problems with more than about 600 securities. To proceed beyond this size, it is often necessary to modify the problem in which case there is typically a loss of information. In this paper, we discuss a computer capability that can exactly compute mean-variance efficient frontiers of problems with up to 2,000 securities in very reasonable time (even if a problem’s covariance matrix is 100% dense). The paper also discusses an augmentation to the theory of portfolio selection that allows multiple objectives (such as dividends, liquidity, social responsibility, amount invested in R&D, and so forth) to be incorporated into the portfolio selection process. In such problems, the efficient set is no longer a “frontier,” but is now best described as a “surface” with the interesting property that it is composed of platelets (like on the back of a turtle). Moreover, the computer capability that can compute the exact efficient frontier of a mean-variance problem with up to 2,000 securities also has, after additional coding, the ability to compute exactly all platelets of the efficient surface of a tri-criterion portfolio problem with up to 400 securities.

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Zusammenfassung  In dieser Arbeit stellen wir einen leistungsf?higen Rechenalgorithmus vor, um den effizienten Rand (die nichtdominierten Alternativen) von Portfolio-Auswahlproblemen in der Finanzierung zu bestimmen. Wir bezeichnen den Berechnungsalgorithmus, der in Java programmiert ist, mit MPQ (multi-parametric quadratic programming). MPQ weist gegenüber bisherigen Berechnungsverfahren eine Reihe von Vorteilen auf: Es kann für umfangreiche Anwendungsf?lle genutzt werden, ist durch passable Rechenzeiten charakterisiert und kann die Menge effizienter Alternativen in einem Bruchteil bisher üblicher Rechenzeiten bestimmen.

     

Stock Evaluation Using a Preference Disaggregation Methodology

This paper presents a real application of a multicriteria decision aid (MCDA) approach to portfolio selection based on preference disaggregation, using ordinal regression and linear programming (UTADIS method; UTilités Additives DIScriminantes). The additive utility functions that are derived through this approach have the extrapolation ability that any new alternative (share) can be easily evaluated and classified into one of several user-predefined groups. The procedure is illustrated with a case study of 98 stocks from the Athens stock exchange, using 15 criteria. The results are encouraging, indicating that the proposed methodology could be used as a tool for the analysis of the portfolio managers' preferences and choices. Furthermore, the comparison with multiple discriminant analysis (either using a stepwise procedure or not) illustrates the superiority of the proposed methodology over a well-known multivariate statistical technique that has been extensively used to study financial decision-making problems.     

含流动性约束及保证金购买的多空投资组合选择模型

本文在基于风险资产的价格服从梯形可能性分布的基础上,引入流动性约束、保证金限制、交易成本和存贷利差等因素,建立了多空投资组合模型。利用非线性规划理论和极大熵方法,给出了求解该模型的一种方法。最后,通过实例验证了主要结果并分析了流动性约束、保证金、交易费和存贷利差等因素对投资组合有效前沿的影响。     

Portfolio Selection Using Stochastic Dominance Criteria

The direct application of stochastic dominance criteria to portfolio selection problems has been thought impractical because an extremely large number of combinations of returns must be considered. This paper proposes and evaluates a rigorous statistical procedure for sampling the combinations of returns on candidate risky assets so that stochastic dominance criteria may be used directly in an efficient linear programming model for portfolio selection. The sampling scheme exploits the association of the return on each candidate stock with the return on a market index in a manner analogous to the Sharpe single-index model, thereby eliminating the large number of combinations with probabilities close to or equalling zero. Portfolios computed by the proposed linear programming stochastic dominance model are compared with those computed by the single-index quadratic programming model, using 180 months of recent data on a sample of NYSE common stocks.     

投资项目集合选择问题的非线性规划模型与解法研究

基于项目集合选择问题的定义,给出了项目集合选择问题求解的一般步骤。依据投资方案组合选择问题的非线性特性,构建了投资项目集合选择问题的非线性规划模型,在此模型的基础上提出了基于外点法求解此类问题的改进贪婪搜索算法。研究了采用surrogate松弛模型确定初始点和运用改进的贪婪算法搜索最优解的具体实现方法,给出了实现算法的具体步骤。     

具有卖空总量限制的多阶段M—SAD投资组合优化

文章提出具有卖空总量限制、阈值约束和V型交易成本的多阶段均值—半绝对偏差（M-SAD）投资组合优化模型。该模型分别运用均值和半绝对偏衡量资产的收益率和风险。由于交易成本的存在,该模型不满足无后效性的动态优化问题。文章将该模型近似为一般动态规划问题,提出一种新的离散迭代方法,并证明该算法是线性收敛的。最后,文章通过实证研究比较分析卖空总量限制和风险偏好系数取不同值时对投资组合最优策略的影响,验证模型和算法的有效性。     

Workload Balancing Through Recurrent Subcontracting

We model a situation where a firm wishes to balance workload requirements by creating a portfolio of recurrent insourcing and outsourcing contracts. We use harmonic analysis to decompose an input workload profile into a portfolio of insourcing and outsourcing contracts using rectangular‐wave basis functions to better achieve some desired constant workload level. However, this initial selection of contracts may result in impractical options. Therefore, we also develop mathematical programs using principles from goal programming and integer programming to refine the portfolio of contracts to more accurately reflect a realistic environment by placing constraints on the available contracts and explicitly considering operational costs. We consider several modeling extensions including the ability to hold limited amounts of inventory and the use of one‐shot contracts to supplement our portfolio of recurrent contracts.     

Selection of supply portfolio under disruption risks

This paper deals with the optimal selection of supply portfolio in a make-to-order environment in the presence of supply chain disruption risks. Given a set of customer orders for products, the decision maker needs to decide from which supplier to purchase custom parts required for each customer order to minimize total cost and mitigate the impact of disruption risks. The selection of suppliers and allocation of orders is based on price and quality of purchased parts and reliability of delivery. The two types of disruption scenarios are considered: scenarios with independent local disruptions of each supplier and scenarios with local and global disruptions that may result in all suppliers disruption simultaneously. The problem is formulated as a single- or bi-objective mixed integer program and a value-at-risk and conditional value-at-risk approach is applied to control the risk of supply disruptions. The proposed portfolio approach is capable of optimizing the supply portfolio by calculating value-at-risk of cost per part and minimizing expected worst-case cost per part simultaneously. Numerical examples are presented and some computational results are reported.     

基于股价预测的泛证券投资组合策略

本文基于期望效用最大化和L₁-中位数估计研究了在线投资组合选择问题。与EG（Exponential Gradient）策略仅利用单期价格信息估计价格趋势不同,本文将利用多期价格信息估计价格趋势,以提高在线策略的性能。首先,基于多期价格数据,利用L₁-中位数估计得到预期价格趋势。然后,通过期望效用最大化,提出一个新的具有线型时间复杂度的在线策略,EGLM（Exponential Gradient via L₁-Median）。并通过相对熵函数定义资产权重向量的距离,进而证明了EGLM策略具有泛证券投资组合性质。最后,利用国内外6个证券市场的历史数据进行实证分析,结果表明相较于UP（Universal Portfolio）策略和EG策略,EGLM策略有更好的竞争性能。