损失厌恶偏好与资产组合选择研究

在不确定性条件下,期望的不可计算性、行动结果比较的局限性以及投资个体选择的非理性使理性假定的选择理论脱离现实,因此重新探讨决策选择准则是必要的.以行为金融理论中不确定性状态下的有限理性与满意准则为依据,引入与满意准则一致且体现损失厌恶偏好的VaR作为风险指标,构建行为资产组合模型,在一种简单新颖的M-V模型的矩阵解法基础上,探寻了正态与部分非正态性假设下VaR-BPT模型的显性最优解或有效前沿,解决了现实中最优投资组合选择的可操作性难题,并在中国股票市场验证了正态性转换方法是处理非正态分布下资产组合选择问题的一种优秀方法.     

考虑保守卖空与财务困境的背景风险投资组合模型

如何合理地考虑投资者所面临的背景风险及现实市场限制来进行有效地投资决策是人们所广泛关注的重要实际管理决策问题。本文研究投资者同时面临加性和乘性两类背景风险的前提下具有保守卖空与财务困境的投资组合选择问题。假定投资者寻求使得投资收益最大、投资风险最小及证券主体财务困境最小的最优投资组合策略,进而提出考虑保守卖空与财务困境的背景风险投资组合模型。然后,利用具有精英策略的非支配排序遗传算法对模型进行求解。最后,通过实例来阐述模型的实用性。研究结果表明:考虑保守卖空能为投资者提供更大的收益;两类背景风险的变化均导致有效前沿面的变化。     

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.     

基于自适应均匀变异人工鱼群投资组合优化算法的研究

投资市场具有一定的风险,影响因素包括经济、政治、市场自身规律等,根据市场机制构建合适的投资组合模型,可以有效降低市场风险,提高投资回报率.人工鱼群算法是模仿自然界鱼类的一种人工智能优化算法,具有较好的优化能力,但有时会陷入局部最优解.首先将人工鱼群算法与均匀变异相结合,加入均匀变异随机数,使算法能够跳出局部最优解,得到全局最优,从而提高算法精度.然后采用改进人工鱼群算法对投资组合模型进行优化求解.实验表明,改进人工鱼群算法具有较好的收敛精度和收敛速度,对投资组合模型的求解效果更好,风险下降,收益增加、     

A risk index model for portfolio selection with returns subject to experts’ estimations

Portfolio selection is concerned with selecting an optimal portfolio that can strike a balance between maximizing the return and minimizing the risk among a large number of securities. Traditionally, security returns were regarded as random variables. However, there are cases that the predictions of security returns are given mainly based on experts’ judgements and estimations rather than historical data. In this paper, we introduce a new type of variable to reflect the subjective estimations of the security returns. A risk index for uncertain portfolio selection is proposed and a new safe criterion for judging the portfolio investment is introduced. Based on the proposed risk index, a new mean-risk index model is developed and its crisp forms are given. In addition, to illustrate the application of the model, two numerical examples are also presented.     

Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint

The complexity of financial markets leads to different types of indeterminate asset returns. For example, asset returns are considered as random variables, when the available data is enough. When the available data is too small or even no available data to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degrees of asset returns. Then, asset returns can be described as uncertain variables. In this paper, we discuss a multi-period portfolio selection problem under uncertain environment, which maximizes the final wealth and minimizes the risk of investment. Unlike the common method to describe the multi-period portfolio selection problem as a bi-objective optimization model, we formulate this uncertain multi-period portfolio selection problem by a new method in three steps with two single objective optimization models. And, we consider the influence of transaction cost and bankruptcy of investor. Then, the proposed uncertain optimization models are transformed into the corresponding crisp optimization models and we use the genetic algorithm combined with penalty function method to solve them. Finally, a numerical example is given to show the effectiveness and practicability of proposed models and method.     

基于鲁棒二阶随机占优的投资组合优化模型研究

本文主要考虑一类经典的含有二阶随机占优约束的投资组合优化问题,其目标为最大化期望收益,同时利用二阶随机占优约束度量风险,满足期望收益二阶随机占优预定的参考目标收益。与传统的二阶随机占优投资组合优化模型不同,本文考虑不确定的投资收益率,并未知其精确的概率分布,但属于某一不确定集合,建立鲁棒二阶随机占优投资组合优化模型,借助鲁棒优化理论,推导出对应的鲁棒等价问题。最后,采用S&P 500股票市场的实际数据,对模型进行不同训练样本规模和不确定集合下的最优投资组合的权重、样本内和样本外不确定参数对期望收益的影响的分析。结果表明,投资收益率在最新的历史数据规模下得出的投资策略,能够获得较高的样本外期望收益,对未来投资更具参考意义。在保证样本内解的最优性的同时,也能取得较高的样本外期望收益和随机占优约束被满足的可行性。     

考虑破产控制的多期模糊资产-负债组合优化模型

在实际的投资决策过程中,一些投资者需要同时管理资产和负债,因此本文研究考虑破产控制和偿债行为的资产-负债管理问题。假设风险资产的收益率和负债的增长率为模糊数,用资产-负债组合的可能性期望和下半绝对偏差度量其收益和风险,以最大化最终期望净财富和最小化最终累积风险为目标,建立了允许限制性卖空的多期模糊资产-负债组合优化模型。然后,设计了一个基于粒子群算法和模拟退火算法的混合智能算法对模型进行求解。最后,通过实例分析说明了所设计算法与传统粒子群算法相比具有更好的优化性能和稳定性。本文所提出策略可以为需要同时管理资产和负债的投资者提供决策支持。     

含有背景风险的双目标投资组合模型研究

投资者进行投资实践时无不面临着背景风险。绝大多数以均值方差为框架的投资组合并没有考虑背景风险,其效用在实际应用中容易受到背景风险的影响。本文在含有交易费用的双目标函数模型中引入背景风险,从是否含有背景风险和背景风险偏好度大小两方面对投资组合问题展开研究,并使用智能算法得到模型的最优解,对模型进行实证分析。实证结果表明:1)当背景风险收益为0时,含有背景风险的投资组合比不含有背景风险的投资组合更能反映真实的投资环境。2) 当背景风险收益不为0时,含有背景风险的投资组合比不含有背景风险的投资组合得到更高的收益。因此,考虑背景风险后投资组合的构建优于不考虑背景风险投资组合的构建。     

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.     

含交易费用的投资组合问题的新模型及其求解途径

本文提出了证券投资组合的一个新模型.该模型综合考虑了证券的收益率、证券分红和证券价格的关系,并将证券分红和证券价格作为系统的随机参数处理,建立了证券投资组合的随机规划模型.利用机会约束规划方法,我们研究了将所建立的随机规划模型转化为普通光滑优化问题求解的方法,得到了该类问题求解的有效途径.     

基于随机因子模型的增强型指数基金

创新性的假设传统的Fama-French三因素模型中的三因素为服从正态分布的随机变量,进而获得了股票收益随机变量的分布信息.采取部分复制的原则建立增强型指数基金随机投资组合优化模型,通过引入投资组合风险概率约束给出增强型指数基金的绝对风险上限,针对增强型指数基金建立基于VaR的超额收益概率约束.引入最买入门槛限制降低增强型指数基金的管理费用,增强其流动性.最后,根据股票收益的概率分布特征,获得基于上述约束的指数基金和增强型指数基金的确定性优化模型,并同时基于上证A股进行了实证分析.     

Credit risk optimization using factor models

We study portfolio credit risk management using factor models, with a focus on optimal portfolio selection based on the tradeoff of expected return and credit risk. We begin with a discussion of factor models and their known analytic properties, paying particular attention to the asymptotic limit of a large, finely grained portfolio. We recall prior results on the convergence of risk measures in this “large portfolio approximation” which are important for credit risk optimization. We then show how the results on the large portfolio approximation can be used to reduce significantly the computational effort required for credit risk optimization. For example, when determining the fraction of capital to be assigned to particular ratings classes, it is sufficient to solve the optimization problem for the large portfolio approximation, rather than for the actual portfolio. This dramatically reduces the dimensionality of the problem, and the amount of computation required for its solution. Numerical results illustrating the application of this principle are also presented. JEL Classification G11     

企业自主研发与合作创新的风险测度及组合优化

企业在整合内部创新要素进行自主研发的同时,也会寻求外部创新资源进行合作创新,当前同时从事多个R&D项目已成为常见的企业经营活动,如何在不确定条件下分析多个R&D项目投资的策略选择及风险优化,对于企业的长期发展具有重要意义。根据企业是否采取合作创新策略,可将其R&D项目分为自主研发与合作创新两类,以项目的研发成功率和投资收益率代表技术风险和市场风险,分别测度自主研发与合作创新项目的风险特性,并在此基础上构建企业R&D项目投资组合优化模型,以在自主研发与合作创新项目之间进行权衡取舍。结果表明,企业对于自主研发与合作创新项目投资组合的最优投资权重,主要取决于这两类组合的期望收益率、收益率方差、期望成功率以及两组合之间的协方差。企业可基于关键参数制定出最优的R&D项目投资组合选择策略,合理分配资金以达到风险最小化的投资目标。     

固定支付下养老基金资产组合CEV模型及最优投资策略

在固定支付水平的条件之下,就养老基金资产组合问题建立常方差弹性(CEV)模型,应用随机控制原理求出了相应的非线性Hamilton-Jacobi-Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题.通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足养老基金既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果.     

An a posteriori decision support methodology for solving the multi-criteria supplier selection problem

This research presents a novel, state-of-the-art methodology for solving a multi-criteria supplier selection problem considering risk and sustainability. It combines multi-objective optimization with the analytic network process to take into account sustainability requirements of a supplier portfolio configuration. To integrate ‘risk’ into the supplier selection problem, we develop a multi-objective optimization model based on the investment portfolio theory introduced by Markowitz. The proposed model is a non-standard portfolio selection problem with four objectives: (1) minimizing the purchasing costs, (2) selecting the supplier portfolio with the highest logistics service, (3) minimizing the supply risk, and (4) ordering as much as possible from those suppliers with outstanding sustainability performance. The optimization model, which has three linear and one quadratic objective function, is solved by an algorithm that analytically computes a set of efficient solutions and provides graphical decision support through a visualization of the complete and exactly-computed Pareto front (a posteriori approach). The possibility of computing all Pareto-optimal supplier portfolios is beneficial for decision makers as they can compare all optimal solutions at once, identify the trade-offs between the criteria, and study how the different objectives of supplier portfolio configuration may be balanced to finally choose the composition that satisfies the purchasing company's strategy best. The approach has been applied to a real-world supplier portfolio configuration case to demonstrate its applicability and to analyze how the consideration of sustainability requirements may affect the traditional supplier selection and purchasing goals in a real-life setting.     

基于排序预测的带交易费用在线投资组合策略

在线投资组合决策过程中频繁调整资产头寸会产生较多的交易费用。本文提出了一个综合考虑预期收益和交易费用的在线投资组合策略。通过预测资产的排序计算组合的预期收益,利用相对熵距离衡量交易费用,构造了一个极大化预期收益和极小化交易费用的优化模型,从而得到了一个在线投资组合更新策略。然后,从理论上证明了该策略具有BH泛证券性,即该策略与离线的最优购买并持有策略具有相同的渐近平均指数收益率。最后,采用中美股票市场实际数据,对该策略进行了数值分析。结果表明,该策略的表现优于已有的在线投资组合策略,且对模型的参数不敏感。     

固定支出下最优资产组合策略

在固定消费支出水平的条件之下,文章就资产组合问题建立常方差弹性（CEV）模型,应用随机控制原理求出了相应的非线性Hamilton—Jacobi—Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题。通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果．     

基于风险网络结构的资产分配策略研究

股票市场是一个高风险市场,如何在频繁发生的极端波动环境下进行有效的资产分配是当前热点问题。本文首次应用VaR模型构建股市风险网络,并基于风险网络模型进行最优投资组合成分选择,分析不同市场波动行情下最优资产分配权重和股票中心性的时变关系,融合风险网络时变中心性和个股表现提出新的动态资产分配策略(φ投资策略)。结果表明:在股市上涨和震荡期,股票中心性和最优投资组合权重呈正相关关系;股市下跌期,股票中心性和最优投资组合权重呈负相关关系;当φ>0.05时,投资者的合理投资区域向高中心性节点移动,反之。φ投资策略的绩效表现证明了风险网络结构能提高投资组合选择过程。此研究对于优化资产配置、提高投资收益、多元化分散投资风险具有重要意义。     

Portfolio Optimization with Stochastic Volatilities and Constraints: An Application in High Dimension

In this paper we are interested in an investment problem with stochastic volatilities and portfolio constraints on amounts. We model the risky assets by jump diffusion processes and we consider an exponential utility function. The objective is to maximize the expected utility from the investor terminal wealth. The value function is known to be a viscosity solution of an integro-differential Hamilton-Jacobi-Bellman (HJB in short) equation which could not be solved when the risky assets number exceeds three. Thanks to an exponential transformation, we reduce the nonlinearity of the HJB equation to a semilinear equation. We prove the existence of a smooth solution to the latter equation and we state a verification theorem which relates this solution to the value function. We present an example that shows the importance of this reduction for numerical study of the optimal portfolio. We then compute the optimal strategy of investment by solving the associated optimization problem.