模糊线性规划在社保基金投资组合优化中的应用

如何选择一个满意的投资组合，在既定条件下实现一个最有效率的风险-收益搭配，是社保基金投资的关键问题，本通过建立和求解社保基金的投资风险最小化模糊线性规划模型和投资收益最大化模糊线性规划模型，试图优化社保基金的投资组合，章最后给出应用示例。     

基于区间数的证券组合投资模型研究

提出了证券组合投资的区间数线性规划模型.通过引入区间数线性规划问题中的目标函数优化水平α和约束水平β将目标函数和约束条件均为区间数的线性规划问题转化为确定型的线性规划问题.投资者可以根据自己的风险喜好程度和客观情况,对这两个参数做出不同的估计,从而得到相应情况下的有效投资方案,使证券组合投资决策更具柔性.最后通过实例分析说明了该模型的可行性.     

区间值模糊线性规划在证券组合投资优化中的应用

针对期望收益率与风险损失率为区间值模糊数的特征,就证券组合投资问题建立了一种区间值模糊线性规划模型,运用一种对区间值模糊数排序的新算法,将模型转化为经典的线性规划问题进行求解,最后通过一个算例说明其有效性和可靠性,为证券组合投资优化问题的解决提供了一种新的方法,对证券组合的理性投资具有重要的指导意义.     

带有初始风险资产的风险投资决策模型

讨论了一类在投资时期初允许带有一部分初始风险资产的风险投资组合决策问题,给出了一个满足总体风险约束下以净收益最大化作为决策目标的资产投资组合的数学规划模型。并由该数学规划的性质,给出该类问题的一个简化的线性规划决策形式。     

投资组合选择的一种模糊决策方法

针对带有V-型交易费用的半绝对偏差风险函数投资组合问题,利用模糊决策理论,提出了一种新的投资收益目标水平和投资风险目标水平心理满意度的非线性隶属函数,并将满足非线性满意程度的投资组合选择模型转化为线性规划模型,证明了两者的等价性,最后通过实例说明了所建模型的可行性与有效性.     

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.     

证券组合投资的多目标区间数线性规划模型

本文提出了证券组合投资的多目标区间数线性规划模型，引入了收益——风险偏好参数和优化水平参数。投资者可以根据对风险的喜好程度和金融市场的客观情况，适当估计这两个参数，从而得到相应情况下的有效投资方案，使投资过程更具柔性，而且更接近于实际情况。     

风险投资组合的线性规划模型

对市场上的多种风险资产和一种无风险资产（存银行）进行组合投资策略的设计需要考虑两个目标:总体收益尽可能大和总体风险尽可能小,而这两个目标在一定意义上是对立的。 本文给出组合投资方案设计的一个线性规划模型,主要思路是通过线性加权综合两个设计目标;假设在投件规模相当大的基础上,将交易费函数近似线性化;通过决策变量的选取化解风险函数的非线性。 模型的最大优点是:计算过程稳定性好,速度快,我们对各种加权因子,求得了最优化决策方案,从而得到问题的有效投资曲线。根据有效投资曲线,投资者可以由自己的主观偏好,直观地选择自己的投资方向。     

证券投资组合优化问题的强健性的锥优化方法(英文)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

含交易费用的证券组合投资模型的满意解

在证券组合投资过程中,忽略交易费用会导致非有效的证券组合投资,本文提出了一个考虑交易费用的证券组合投资的区间数线性规划模型,通过引入区间数线性规划问题中的目标函数优化水平参数λ和约束条件满足水平参数η将目标函数和约束条件均为区间数的区间数线性规划模型转化为确定型的一般线性规划模型,进而求得相应于优化水平λ和满足水平η的满意解.     

A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation

We present a new approach to asset allocation with transaction costs. A multiperiod stochastic linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by the model that balances expected return and risk. Utilizing portfolio protection and dynamic hedging, an investment portfolio similar to an option-like payoff structure on the initial investment portfolio is characterized. The relative changes in the expected terminal wealth, worst case payoff, and risk aversion, are studied theoretically and illustrated using a numerical example. This model dominates a static mean-variance model when the optimal portfolios are evaluated by the Sharpe ratio. Received: August 15, 1999 / Accepted: October 1, 2000?Published online December 15, 2000     

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.     

Portfolio selection with a minimax measure in safety constraint

In this paper, we attempt to design a portfolio optimization model for investors who desire to minimize the variation around the mean return and at the same time wish to achieve better return than the worst possible return realization at every time point in a single period portfolio investment. The portfolio is to be selected from the risky assets in the equity market. Since the minimax portfolio optimization model provides us with the portfolio that maximizes (minimizes) the worst return (worst loss) realization in the investment horizon period, in order to safeguard the interest of investors, the optimal value of the minimax optimization model is used to design a constraint in the mean-absolute semideviation model. This constraint can be viewed as a safety strategy adopted by an investor. Thus, our proposed bi-objective linear programming model involves mean return as a reward and mean-absolute semideviation as a risk in the objective function and minimax as a safety constraint, which enables a trade off between return and risk with a fixed safety value. The efficient frontier of the model is generated using the augmented -constraint method on the GAMS software. We simultaneously solve the ratio optimization problem which maximizes the ratio of mean return over mean-absolute semideviation with same minimax value in the safety constraint. Subsequently, we choose two portfolios on the above generated efficient frontier such that the risk from one of them is less and the mean return from other portfolio is more than the respective quantities of the optimal portfolio from the ratio optimization model. Extensive computational results and in-sample and out-of-sample analysis are provided to compare the financial performance of the optimal portfolios selected by our proposed model with that of the optimal portfolios from the existing minimax and mean-absolute semideviation portfolio optimization models on real data from S&P CNX Nifty index.     

非负约束条件下组合证券投资决策的分枝定界法

研究非负约束条件下 ,实现预期收益率的组合证券投资决策问题 ,将整数线性规划的分枝定界法用于该问题的求解 ,并应用于一个四元证券投资决策问题     

多约束的多阶段积极投资组合模型及实证研究

构建投资组合时需要衡量其风险,除了考虑组合本身的风险暴露,还需考虑其相对基准组合的风险暴露.再者,确定组合权重时需要根据市场的规则加入合适的约束.基于此,为了较为完整地考虑现实投资组合面临的风险及交易约束,将绝对风险(CVaR)和相对风险(跟踪误差)作为风险约束,将交易成本、卖空限制和多元权值作为交易限制约束,构建一个新的多阶段投资组合模型,并利用动态规划和非线性优化方法进行求解.最后,利用上证50成分股中41只股票构建投资组合进行实证研究.实证结果表明构建的多阶段投资组合模型能持续战胜基准组合且优于单阶段投资组合,同时也表明模型考虑多元权值约束具有现实意义.     

Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.     

证券投资组合优化问题的强健性的锥优化方法(英)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

Mean-variance models for portfolio selection with fuzzy random returns

This paper develops two novel types of mean-variance models for portfolio selection problems, in which the security returns are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. In the proposed models, we take the expected return of a portfolio as the investment return and the variance of the expected return of a portfolio as the investment risk. We assume that the security returns are triangular fuzzy random variables. To solve the proposed portfolio problems, this paper first presents the variance formulas for triangular fuzzy random variables. Then this paper applies the variance formulas to the proposed models so that the original portfolio problems can be reduced to nonlinear programming ones. Due to the reduced programming problems include standard normal distribution in the objective functions, we cannot employ the conventional solution methods to solve them. To overcome this difficulty, this paper employs genetic algorithm (GA) to solve them, and verify the obtained optimal solutions via Kuhn-Tucker (K-T) conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed models and methods.