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。     

具有现实约束的均值-方差模糊投资组合绩效评价

本文提出了具有实际约束的均值-方差模糊投资组合优化模型。由于实际投资约束情况,如交易成本、交易量限制、借款限制和基数约束的影响,投资组合优化模型非常复杂,难以获得真实前沿面的解析解,这给投资组合理论的应用带来了很大的困难。基于数据的实际约束的均值-方差模糊投资组合DEA评价模型,文章通过构造前沿面来逼近一般情形下真实的前沿面。最后,通过上海证券市场的实际数据验证了本文方法的合理性与可行性。     

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DEA交叉效率的投资组合优化策略

以风险报酬比指标中的风险和收益因子作为投入产出,利用BCC模型计算投资效率.然后引入交叉效率模型,在均值方差框架下计算最优投资组合,将其形成投资策略在A股市场中回测.以传统的全局最小方差模型、纯交叉效率模型、等权模型和大盘指数作为业绩比较基准,回测结果发现不论是否放开卖空约束,投资组合策略均可以跑赢所有基准.稳定性测试表明,在不同调仓周期和不同的指数成分股中,投资组合策略仍然表现稳健,可以跑赢基准.     

基于模糊收益率的组合投资模型

本文考虑了收益率为模糊数的投资组合选择问题,利用模型约束简化方差约束,建立了投资组合选择的模糊线性规划模型,然后引进模糊期望把模糊线性规划问题化为普通参数线性规划问题,最后给出了一个数值算例.     

限制性卖空的均值-方差投资组合优化

本文提出了限制性卖空的均值-方差投资组合模型,通过变量替换将该模型转变为一般二次规划问题,从而运用不等式组的旋转算法进行求解.文章还以一个具体例子验证该算法的有效性,并证明在一定变化范围内,借入资产的资金与总资金的比例越大越有助于拓展投资机会空间.     

风险资产价格服从CEV模型的投资组合随机微分博弈

本文在风险资产价格服从CEV模型时,讨论两个投资者的时间一致均值-方差最优投资组合选择的随机微分博弈问题.运用动态规划原理,求得了最优投资策略及相应的值函数.     

投资组合模型的改进研究:基于企业社会责任视角的实证分析

在尊重和借鉴前人对企业社会责任研究,尤其是在企业社会责任评价研究基础之上,本文从投资者的角度在投资组合过程中研究企业社会责任。在Markowitz(均值—方差)理论模型上添加企业社会责任的三个一级指标期望作为目标函数,由此将传统的投资组合模型扩展为五个目标函数的投资组合选择模型,而且我们根据经济学中经典的效用函数理论证明了此模型的正确性。本文引入主流的企业社会责任评价标准,并对一些典型公司进行打分量化。在此基础之上建立了以期望回报率、回报率的方差、核心利益相关者期望、蛰伏利益相关者期望和边缘利益相关者期望为目标函数的投资组合选择模型,在最小方差曲面上选取10个点构造投资组合,并以样本外的数据验证了模型的有效性。研究发现:根据此模型计算出来的部分投资组合回报率显著高于同期的市场指数。研究结果表明,这种关注企业社会责任的多目标投资组合选择模型,不仅让投资者可以直接控制企业社会责任,而且实际数据证明了此模型的优势之处,从而为关注企业社会责任的投资者提供一种投资的方法和思路。     

具有实际约束的多阶段M-V投资组合时间一致性策略研究

从动态规划的角度分析,方差算子的不可分离性导致标准的多阶段均值-方差模型的最优投资策略不满足时间一致性。文章采用条件期望映射的方法,构建了一个具有交易成本、借贷约束和阈值约束的多阶段M-V投资组合模型。由于考虑了交易成本,该模型是一个具有路径依赖性的动态优化问题。为了获得其时间一致性投资策略,文章将该问题近似地转化为连续性动态规划模型,证明最优解的近似度,并运用离散迭代算法求解。最后,使用上海证券交易所的部分历史数据验证了模型和算法的有效性。     

模糊投资组合选择问题的改进帝企鹅优化算法

模糊投资组合选择问题是在基本投资组合模型中引入模糊集理论,使所建立的模型与实际市场更加吻合,但同时也增加了模型求解难度.因此,本文针对两种不同的模糊投资组合模型,提出一种改进帝企鹅优化算法.算法首先引入可行性准则,处理模糊投资组合模型中的约束.其次,算法中加入变异机制,平衡算法的开发和探索能力,引导种群向最优个体收敛.通过对CEC 2006中的13个标准测试问题及两个模糊投资组合问题实例进行数值实验,并与其他群智能优化算法进行结果比较,发现本文所提出的算法具有较好的优化性能,并且对于求解模糊投资组合选择问题是有效的.     

Probability maximization models for portfolio selection under ambiguity

This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers’ predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model.     

A Class of Chance Constrained Multi-objective Portfolio Selection Model Under Fuzzy Random Environment

This paper deals with a class of chance constrained portfolio selection problems in the fuzzy random decision making system. An integrated fuzzy random portfolio selection model with a chance constraint is proposed on the basis of the mean-variance model and the safety-first model. According to different definitions of chance, we consider two types of fuzzy random portfolio selection models: one is for the optimistic investors and the other is for the pessimistic investors. In order to deal with the fuzzy random models, we develop a few theorems on the variances of fuzzy random returns and the equivalent partitions of two types of chance constraints. We then transform the fuzzy random portfolio selection models into their equivalent crisp models. We further employ the ε-constraint method to obtain the efficient frontier. Finally, we apply the proposed models and approaches to the Chinese stock market as an illustration.     

On portfolio optimization using fuzzy decisions

We consider stochastic optimization problems involving stochastic dominance constraints. We develop portfolio optimization model involving stochastic dominance constrains using fuzzy decisions and we concentrate on fuzzy linear programming problems with only fuzzy technological coefficients and aplication/implementation of modified subgradient method to fuzy linear programming problems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Risk optimization with p-order conic constraints: A linear programming approach

The paper considers solving of linear programming problems with p-order conic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints. The proposed approach is based on construction of polyhedral approximations for p-order cones, and then invoking a Benders decomposition scheme that allows for efficient solving of the approximating problems. The conducted case study of portfolio optimization with p-order conic constraints demonstrates that the developed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.     

Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization

Inspired by the successful applications of the stochastic optimization with second order stochastic dominance (SSD) model in portfolio optimization, we study new numerical methods for a general SSD model where the underlying functions are not necessarily linear. Specifically, we penalize the SSD constraints to the objective under Slater’s constraint qualification and then apply the well known stochastic approximation (SA) method and the level function method to solve the penalized problem. Both methods are iterative: the former requires to calculate an approximate subgradient of the objective function of the penalized problem at each iterate while the latter requires to calculate a subgradient. Under some moderate conditions, we show that w.p.1 the sequence of approximated solutions generated by the SA method converges to an optimal solution of the true problem. As for the level function method, the convergence is deterministic and in some cases we are able to estimate the number of iterations for a given precision. Both methods are applied to portfolio optimization problem where the return functions are not necessarily linear and some numerical test results are reported.     

Portfolio construction based on stochastic dominance and target return distributions

Mean-risk models have been widely used in portfolio optimization. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is non-dominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective functions. A model is proposed in which the aspiration points relate to ordered outcomes for the portfolio return. This concept is extended by additionally specifying reservation points, which act pre-emptively in the optimization model. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated.     

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。     

Robustness of optimal portfolios under risk and stochastic dominance constraints

Solutions of portfolio optimization problems are often influenced by a model misspecification or by errors due to approximation, estimation and incomplete information. The obtained results, recommendations for the risk and portfolio manager, should be then carefully analyzed. We shall deal with output analysis and stress testing with respect to uncertainty or perturbations of input data for static risk constrained portfolio optimization problems by means of the contamination technique. Dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of convexity-based global contamination bounds. Results obtained in our paper [Dupa?ová, J., & Kopa, M. (2012). Robustness in stochastic programs with risk constraints. Annals of Operations Research, 200, 55–74.] were derived for the risk and second order stochastic dominance constraints under suitable smoothness and/or convexity assumptions that are fulfilled, e.g. for the Markowitz mean–variance model. In this paper we relax these assumptions having in mind the first order stochastic dominance and probabilistic risk constraints. Local bounds for problems of a special structure are obtained. Under suitable conditions on the structure of the problem and for discrete distributions we shall exploit the contamination technique to derive a new robust first order stochastic dominance portfolio efficiency test.     

Scenario optimization

Uncertainty in the parameters of a mathematical program may present a modeller with considerable difficulties. Most approaches in the stochastic programming literature place an apparent heavy data and computational burden on the user and as such are often intractable. Moreover, the models themselves are difficult to understand. This probably explains why one seldom sees a fundamentally stochastic model being solved using stochastic programming techniques. Instead, it is common practice to solve a deterministic model with different assumed scenarios for the random coefficients. In this paper we present a simple approach to solving a stochastic model, based on a particular method for combining such scenario solutions into a single, feasible policy. The approach is computationally simple and easy to understand. Because of its generality, it can handle multiple competing objectives, complex stochastic constraints and may be applied in contexts other than optimization. To illustrate our model, we consider two distinct, important applications: the optimal management of a hydro-thermal generating system and an application taken from portfolio optimization.     

Genetic algorithms for portfolio selection problems with minimum transaction lots

Conventionally, portfolio selection problems are solved with quadratic or linear programming models. However, the solutions obtained by these methods are in real numbers and difficult to implement because each asset usually has its minimum transaction lot. Methods considering minimum transaction lots were developed based on some linear portfolio optimization models. However, no study has ever investigated the minimum transaction lot problem in portfolio optimization based on Markowitz’ model, which is probably the most well-known and widely used. Based on Markowitz’ model, this study presents three possible models for portfolio selection problems with minimum transaction lots, and devises corresponding genetic algorithms to obtain the solutions. The results of the empirical study show that the portfolios obtained using the proposed algorithms are very close to the efficient frontier, indicating that the proposed method can obtain near optimal and also practically feasible solutions to the portfolio selection problem in an acceptable short time. One model that is based on a fuzzy multi-objective decision-making approach is highly recommended because of its adaptability and simplicity.