How to support the application of multiple criteria decision analysis? Let us start with a comprehensive taxonomy

Decision making is a complex task that involves a multitude of perspectives, constraints, and variables. Multiple Criteria Decision Analysis (MCDA) is a process that has been used for several decades to support decision making. It includes a series of steps that systematically help Decision Maker(s) (DM(s)) and stakeholders in structuring a decision making problem, identifying their preferences, and building a decision recommendation consistent with those preferences. Over the last decades, many studies have demonstrated the conduct of the MCDA process and how to select an MCDA method. Until now, there has not been a review of these studies, nor a proposal of a unified and comprehensive high-level representation of the MCDA process characteristics (i.e., features), which is the goal of this paper. We introduce a review of the research that defines how to conduct the MCDA process, compares MCDA methods, and presents Decision Support Systems (DSSs) to recommend a relevant MCDA method or a subset of methods. We then synthesize this research into a taxonomy of characteristics of the MCDA process, grouped into three main phases, (i) problem formulation, (ii) construction of the decision recommendation, and (iii) qualitative features and technical support. Each of these phases includes a subset of the 10 characteristics that helps the analyst implementing the MCDA process, while also being aware of the implication of these choices at each step. By showing how decision making can be split into manageable and justifiable steps, we reduce the risk of overwhelming the analyst, as well as the DMs/stakeholders during the MCDA process. A questioning strategy is also proposed to demonstrate how to apply the taxonomy to map MCDA methods and select the most relevant one(s) using real case studies. Additionally, we show how the DSSs for MCDA method recommendation can be grouped into three main clusters. This proposal can enhance a traceable and categorizable development of such systems.     

Risk‐Based Sampling: I Don't Want to Weight in Vain

Recently, there has been considerable interest in developing risk‐based sampling for food safety and animal and plant health for efficient allocation of inspection and surveillance resources. The problem of risk‐based sampling allocation presents a challenge similar to financial portfolio analysis. Markowitz (1952) laid the foundation for modern portfolio theory based on mean‐variance optimization. However, a persistent challenge in implementing portfolio optimization is the problem of estimation error, leading to false “optimal” portfolios and unstable asset weights. In some cases, portfolio diversification based on simple heuristics (e.g., equal allocation) has better out‐of‐sample performance than complex portfolio optimization methods due to estimation uncertainty. Even for portfolios with a modest number of assets, the estimation window required for true optimization may imply an implausibly long stationary period. The implications for risk‐based sampling are illustrated by a simple simulation model of lot inspection for a small, heterogeneous group of producers.     

Evaluating the quality of solutions in project portfolio selection

Assessing the quality of decisions while selecting project portfolios becomes an inherent part of the decision-making process when the project parameters are inaccurate or uncertain. Small adjustments to the initial parameters can lead to situations where the preferred portfolio no longer reflects the investor’s requirements. The paper studies the post-optimal analysis of the Pareto optimal portfolios chosen by Savage’s risk criteria. Stability characteristic, such as the stability function, is considered. Using the stability function, we evaluate the quality of feasible portfolios. This function indicates the robustness of portfolios to any changes in the initial data. Using the stability function the formula for calculating the optimality threshold is obtained, which determines the level of risk reduction when the selected Pareto optimal portfolio can obtain optimal properties. The performances of the stability function and the optimality threshold are shown in the case study using global risk assessments for projects participating in the Belt and Road Initiative. The computation results demonstrate the ability through the stability function to evaluate the quality and optimal properties of feasible project portfolios.     

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.     

考虑交易成本的多阶段投资组合评价方法研究

多阶段投资组合评价是目前研究的热点问题,本文将交易成本考虑进去,构建了考虑交易成本的多阶段投资组合优化模型,基于真实前沿面定义了投资组合的效率并构建了相应的非线性模型进行计算。针对非线性模型难以求解及真实前沿面解析解难以获得等问题,本文证明了前沿面函数为凹函数,进而利用DEA模型的前沿面来逼近真实前沿面并估计多阶段投资组合的效率,最后通过仿真分析验证了本文方法的有效性。     

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。     

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.     

多属性隐式变权决策分析方法

为克服多因素变权决策方法的内在缺陷,基于Belton 和Gear提出的B/G-AHP层次分析原理给出了一种隐含式的多属性变权决策建模思想,并运用该思想给出了一种多属性变权决策新方法。它相对于多因素变权决策方法具有三方面的比较优势。其一,依赖的变权偏好信息直接由决策者给出,因而能够克服决策分析者对决策结果的主观武断性影响,更好地反映决策者的真实偏好。其二,不会受到由因素的属性值转化为偏好值所额外引入的主观测度偏差的干扰。其三,对决策者主观判断可能存在的误差予以了旨在弱化其影响的优化控制。数值分析表明新方法拥有较好的变权能力,并且相对于已有方法能够给出更易为决策者所接受的评价结论,因而具有较好的应用有效性。     

惯性因子跟踪策略的有效性：来自中国股票市场的证据

基于惯性/反转效应普遍存在的现象以及中国股票市场上不能直接实施惯性/反转投资策略的事实,提出能灵活抓住惯性/反转效应的惯性因子跟踪策略。通过建立和求解惯性因子跟踪策略模型,我们发现,在允许卖空的条件下,最优惯性因子跟踪组合满足两基金分离定理,两基金分别是惯性因子模仿组合和最小方差组合。选择沪深300十大行业指数作为风险资产的代表,实证考察惯性因子跟踪组合的业绩,并与等权组合和最小方差组合的业绩进行比较。结果发现：惯性因子跟踪组合可以在保持和等权组合、最小方差组合风险水平相当的情况下带来更高的收益水平和夏普比率,平均而言,惯性因子跟踪组合的年化超额收益率(8.88%)比等权组合的年化超额收益率高出3.7%,夏普比率(0.42)高出0.18;即便在考虑交易成本的情况下,惯性因子跟踪组合的净夏普比率仍然高出等权组合0.16;综合上方获利和下方风险控制两个方面看,惯性因子跟踪组合优于等权组合。惯性因子跟踪策略的有效性相对于惯性因子的计算方法和样本数据选择区间具有稳健性。     

A robust ranking method extending ELECTRE III to hierarchy of interacting criteria,imprecise weights and stochastic analysis

A great majority of methods designed for Multiple Criteria Decision Aiding (MCDA) assume that all assessment criteria are considered at the same level, however, decision problems encountered in practice often impose a hierarchical structure of criteria. The hierarchy helps to decompose complex decision problems into smaller and manageable subtasks, and thus, it is very attractive for computational efficiency and explanatory purposes. To handle the hierarchy of criteria in MCDA, a methodology called Multiple Criteria Hierarchy Process (MCHP), has been recently proposed. MCHP permits to consider preference relations with respect to a subset of criteria at any level of the hierarchy. Here, we propose to apply MCHP to the ELECTRE III ranking method adapted to handle three types of interaction effects between criteria: mutual-weakening, mutual-strengthening and antagonistic effect. We also involve in MCHP an imprecise elicitation of criteria weights, generalizing a technique called the SRF method. In order to explore the plurality of rankings obtained by the ELECTRE III method for possible sets of criteria weights, we apply the Stochastic Multiobjective Acceptability Analysis (SMAA) that permits to draw robust conclusions in terms of rankings and preference relations at each level of the hierarchy of criteria. The novelty of the whole methodology consists of a joint consideration of hierarchical assessments of alternatives performances on interacting criteria, imprecise criteria weights, and robust analysis of ranking recommendations resulting from ELECTRE III. An example regarding the multiple criteria ranking of some European universities will show how to apply the proposed methodology on a decision problem.     

Multiple Criteria Hierarchy Process with ELECTRE and PROMETHEE

Robust Ordinal Regression (ROR) supports Multiple Criteria Decision Process by considering all sets of parameters of an assumed preference model, that are compatible with preference information elicited by a Decision Maker (DM). As a result of ROR, one gets necessary and possible preference relations in the set of alternatives, which hold for all compatible sets of parameters, or for at least one compatible set of parameters, respectively. In this paper, we propose an extension of ELECTRE and PROMETHEE methods to the case of the hierarchy of criteria, which was never considered before. Then, we adapt ROR to the hierarchical versions of ELECTRE and PROMETHEE methods.     

Incorporating Black-Litterman views in portfolio construction when stock returns are a mixture of normals

In this paper, we consider the basic problem of portfolio construction in financial engineering, and analyze how market-based and analytical approaches can be combined to obtain efficient portfolios. As a first step in our analysis, we model the asset returns as a random variable distributed according to a mixture of normal random variables. We then discuss how to construct portfolios that minimize the Conditional Value-at-Risk (CVaR) under this probabilistic model via a convex program. We also construct a second-order cone representable approximation of the CVaR under the mixture model, and demonstrate its theoretical and empirical accuracy. Furthermore, we incorporate the market equilibrium information into this procedure through the well-known Black-Litterman approach via an inverse optimization framework by utilizing the proposed approximation. Our computational experiments on a real dataset show that this approach with an emphasis on the market equilibrium typically yields less risky portfolios than a purely market-based portfolio while producing similar returns on average.     

The business portfolio approach—Where it falls down in practice

During the past decade the SBU (or portfolio) concept has enjoyed widespread popularity as a basis for corporate-wide strategic planning systems within large, diversified firms. This article discusses the implementation of such systems on the basis of 3 years of clinical and small sample research. A ‘basic model’ of implementation is used as a basis for comparison to progressive practice as observed in a sample of 13 firms. Furthermore, a new conceptual perspective for the portfolio concept is developed as a complement to the observed approach to implementation.     

Making more of alliance portfolios: The role of alliance portfolio coordination

Alliance portfolios enable firms to access and integrate multiple resources from different, simultaneous partners. We assess the extent to which alliance portfolio coordination benefits focal firms along three alliance portfolio characteristics: alliance portfolio size, the complementarity of the resources available through the portfolio, and the degree to which relation-specific investments are made across the portfolio. Based on a questionnaire completed by 444 Dutch companies, we found that the three portfolio characteristics play an important role in creating benefits for focal firms through their portfolios. Additionally, our findings suggest that alliance portfolio coordination is an important element in dealing with the challenge of managing portfolios, in that it shapes the effect of the other portfolio characteristics.     

Efficient Semiparametric Estimation of Quantile Treatment Effects

This paper develops estimators for quantile treatment effects under the identifying restriction that selection to treatment is based on observable characteristics. Identification is achieved without requiring computation of the conditional quantiles of the potential outcomes. Instead, the identification results for the marginal quantiles lead to an estimation procedure for the quantile treatment effect parameters that has two steps: nonparametric estimation of the propensity score and computation of the difference between the solutions of two separate minimization problems. Root‐N consistency, asymptotic normality, and achievement of the semiparametric efficiency bound are shown for that estimator. A consistent estimation procedure for the variance is also presented. Finally, the method developed here is applied to evaluation of a job training program and to a Monte Carlo exercise. Results from the empirical application indicate that the method works relatively well even for a data set with limited overlap between treated and controls in the support of covariates. The Monte Carlo study shows that, for a relatively small sample size, the method produces estimates with good precision and low bias, especially for middle quantiles.     

耦合风险视角下基于GARCH-Copula模型的基金组合风险研究

在资本市场不断多样化的投资方式中, 投资组合以其相对稳定的风险与收益而得到广泛应用, 其中基金组合凭借在收益一定的情况下的低风险成为投资者关注的热门品种.传统的投资组合研究大多只考虑市场风险的影响, 忽略了信用风险的耦合效应, 从而往往导致对组合总体风险的低估.首先借助于GARCH模型获得边缘分布, 然后选择Copula函数刻画各基金之间的相关结构, 建立联合分布模型, 进而采用Monte Carlo方法模拟生成基金组合中各基金的收益率序列, 最后根据损失函数计算基金组合的风险价值.实证结果表明, 市场风险大的基金组合其信用风险不一定大, 并且基金组合能有效分散基金风险.同时, 耦合风险视角下基金组合的CVaR值大于市场风险视角下的CVaR值, 耦合风险能更好地衡量基金组合的风险.另外, Student t-Copula模型较之其它模型能更好地刻画耦合风险的联合相依结构.     

Nature-inspired metaheuristics for multiobjective activity crashing

Many project tasks and manufacturing processes consist of interdependent time-related activities that can be represented as networks. Deciding which of these sub-processes should receive extra resources to speed up the whole network (i.e., where activity crashing should be applied) usually involves the pursuit of multiple objectives amid a lack of a priori preference information. A common decision support approach lies in first determining efficient combinations of activity crashing measures and then pursuing an interactive exploration of this space. As it is impossible to exactly solve the underlying multiobjective combinatorial optimization problem within a reasonable computation time for real-world problems, we have developed proper solution procedures based on three major (nature-inspired) metaheuristics. This paper describes these implementations, discusses their strengths, and provides results from computational experiments.     

Absolute return portfolios

In this paper we consider the problem of selecting an absolute return portfolio. This is a portfolio of assets that is designed to deliver a good return irrespective of how the underlying market (typically as represented by a market index) performs. We present a three-stage mixed-integer zero-one program for the problem that explicitly considers transaction costs associated with trading. The first two stages relate to a regression of portfolio return against time, whilst the third stage relates to minimising transaction cost.We extend our approach to the problem of designing portfolios with differing characteristics. In particular we present models for enhanced indexation (relative return) portfolios and for portfolios that are a mix of absolute and relative return. Computational results are given for portfolios derived from universes defined by S&P international equity indices.     

Evaluation of Multicriteria Decision Analysis Algorithms in Food Safety: A Case Study on Emerging Zoonoses Prioritization

Decision making in food safety is a complex process that involves several criteria of different nature like the expected reduction in the number of illnesses, the potential economic or health-related cost, or even the environmental impact of a given policy or intervention. Several multicriteria decision analysis (MCDA) algorithms are currently used, mostly individually, in food safety to rank different options in a multifactorial environment. However, the selection of the MCDA algorithm is a decision problem on its own because different methods calculate different rankings. The aim of this study was to compare the impact of different uncertainty sources on the rankings of MCDA problems in the context of food safety. For that purpose, a previously published data set on emerging zoonoses in the Netherlands was used to compare different MCDA algorithms: MMOORA, TOPSIS, VIKOR, WASPAS, and ELECTRE III. The rankings were calculated with and without considering uncertainty (using fuzzy sets), to assess the importance of this factor. The rankings obtained differed between algorithms, emphasizing that the selection of the MCDA method had a relevant impact in the rankings. Furthermore, considering uncertainty in the ranking had a high influence on the results. Both factors were more relevant than the weights associated with each criterion in this case study. A hierarchical clustering method was suggested to aggregate results obtained by the different algorithms. This complementary step seems to be a promising way to decrease extreme difference among algorithms and could provide a strong added value in the decision-making process.     

A case-based distance method for screening in multiple-criteria decision aid

Screening is a process of multiple-criteria decision aid (MCDA) in which a large set of alternatives is reduced to a smaller set that most likely contains the best choice. We propose screening using a distance model calibrated on the basis of the decision-maker's own judgement. Viewing MCDA as preference aggregation based on consequence data, we define consequence and preference expressions (values and weights) and describe how they are aggregated. Then we define screening and explain some of its properties. Using an appropriate definition of distance, our case-based distance method screens a set of alternatives using criterion weights and a distance threshold obtained by quadratic optimization using the decision-maker's selection of alternatives from a test set. This case-based method can elicit the decision maker's preferences more expeditiously and accurately than direct inquiry. An application in water supply planning is used to demonstrate the procedure.