CVaR 投资组合问题求解的一种混合元启发式搜索算法

本文针对均值-CVaR投资组合优化问题,基于混沌搜索、粒子群优化和引力搜索算法提出了一种新的混合元启发式搜索算法,而后基于多维布朗运动,借助Monte Carlo模拟情景生成得到价格路径,进而近似求解均值-CVaR投资组合选择问题,并与线性规划和非参数估计两种求解算法进行比较。模拟和实证算例结果表明,新算法在求解有效性和实用性方面表现更好,取得更为满意的结果。     

CVaR鲁棒均值-CVaR投资组合模型与求解

传统的均值-风险(包括方差、VaR、CVaR等)组合选择模型在计算最优投资组合时,常假定均值是已知的常值,但在实际资产配置中,收益的均值估计会有偏差,即存在着估计风险.在利用CVaR测度估计风险的基础上,研究了CVaR鲁棒均值-CVaR投资组合选择模型,给出了另外两种不同的求解方法,即对偶法和光滑优化方法,并探讨了它们的相关性质及特征,数值实验表明在求解大样本或者大规模投资组合选择问题上,对偶法和光滑优化方法在计算上是可行且有效的.     

鲁棒均值-CVaR投资组合模型及实证:基于安全准则的视角

考虑证券市场的不确定性,将资产的收益率看成区间随机变量。利用鲁棒优化方法,构建鲁棒均值-CVaR投资组合模型。采用对偶理论,将鲁棒均值-CVaR投资组合模型转换为线性规划问题,降低了模型的求解难度,有助于计算大规模的资产组合。进一步地,考虑投资者的安全性需求,在模型中引入最大违反概率,控制模型的保守程度,并直观反映投资者的安全性要求。采用实证的方法,研究模型的有效性。结果表明:鲁棒均值-CVaR投资组合模型具有较好的稳健性,且满足投资者的安全性要求,在实际的投资决策中具有可行性。     

均值-CVaR模型的稳健构建方法及其比较研究

传统均值-CVaR模型具有不稳健性,当样本数据存在离群值时,传统均值-CVaR模型获得的投资效果可能会偏离实际情况。针对这一现象,文中将稳健统计思想与传统均值-CVaR模型相结合,构建出稳健均值-CVaR模型以削弱或消除离群值的影响,从而获得较为可靠的投资效果。为了说明稳健改进方法的有效性和可行性,文中进行了模拟实验和实证分析,结果均表明:当数据中不存在离群值时,传统和稳健均值-CVaR模型获得的投资效果基本保持一致;但当数据中存在离群值时,传统均值-CVaR模型获得的投资效果与实际不符,而稳健均值-CVaR模型获得的投资效果仍保持着良好的一致性,说明稳健均值-CVaR模型对离群值具有较好的抗差性和抗干扰性。     

基于GARCH类模型的空头市场情景生成与投资组合

2015年中,中国股票市场经历了一轮较强的空头市场,投资者面临市场价格的极大不确定性.而若能有效模拟此类型市场收益波动,对于投资者优化金融决策有积极意义.文章试验了当前主要的几种非对称GARCH类模型及多种残差分布模型,最后发现,利用ARMA-EGARCH-SSTD的组合模型能较好地模拟空头股票数据收益率效果.同时文中采用中国股票市场数据进行算例分析,发现将GARCH类模型情景拟合结果与均值-CVaR模型结合得到的投资组合优化方法能有效管理空头市场环境下的投资组合风险.     

多目标条件风险值的一种近似求解方法

本文研究了一种求解多目标条件风险值问题的近似方法,首先引入了多个损失函数在对应的置信水平下关于一个证券组合的α-VaR损失值,以及α-CVaR损失值概念．α-CVaR损失值表明了在给定的证券组合于置信水平对应的最小信用风险值的条件期望损失值,那么求出这样的最小条件期望损失值的模型构成了一个求解α-CVaR损失值的多目标问题,它的解就是最小条件期望损失值的有效证券组合,即Pareto弱有效解．为了求解它的Pareto弱有效解,我们引进了损失函数对应的优化问题(SCVaR),可以通过求解非线性规划问题(SCVaR)的最优解近似地刻画α—CVaR损失值,这样使得求解α-CVaR损失值变得容易．     

资产组合优化的多分形模型及实证分析

将马尔科夫转换多分形模型引入均值-CVaR框架,构建资产组合优化的多分形模型,并给出最优组合投资策略的求解步骤.实证分析结果表明,基于多分形模型的组合策略在描述性统计分析、风险调整收益分析、经济表现分析以及策略稳定性分析中的表现均优于基于CCC-GARCH模型的组合策略,考虑多分形性确实有助于改善资产组合策略.文章所构建的模型和实证结果为资产组合投资实践提供了有益的参考.     

基于高频波动率模型与R-vine copula的行业资产组合风险测度研究

相较于低频波动率模型,高频波动率模型在单资产的波动和风险预测中均取得了更好效果,因此如何将高频波动率模型引入组合风险分析具有重要的理论和现实意义。本文以沪深300指数中的6种行业高频数据为例,运用滚动时间窗技术建立9类已实现波动率异质自回归(HAR-RV-type)模型刻画行业指数波动,同时使用R-vine copula模型描述行业资产间相依结构,进一步结合均值-CVaR模型优化行业资产组合投资比例,构建组合风险的预期损失模型,并通过返回测试比较不同风险模型的精度差异。研究结果表明:将HAR族高频波动率模型引入组合风险分析框架,能够有效预测行业资产组合风险状况;高频波动率预测的准确性将进而影响组合风险测度效果,跳跃、符号跳跃变差以及符号正向、负向跳跃变差均有助于提高行业组合风险的预测精度。     

协方差矩阵退化情形均值-CVaR模型的有效边界

本文利用CVaR方法代替方差或CVaR来度量风险,建立了均值-CVaR模型,首先利用等CVaR线的方法研究了包含无风险资产的均值-CVaR模型的有效边界,然后在无套利假设下研究了当风险资产的协方差矩阵是奇异时的均值-CVaR模型,并得到了正态情形下模型的有效边界及其解析表达式.     

双边Burr分布及其在金融市场风险预测与优化中的应用

考虑到金融数据具有非对称、尖峰厚尾特征,文章将具有尖峰厚尾特征的Burr分布拓展至双边Burr(TSB)分布,给出了其重要的数字特征、极大似然估计、最小二乘估计以及加权最小二乘估计,并通过数值模拟验证了这三种参数估计方法的有效性.其次,文章基于TSB分布构建GJR-GARCH模型,旨在研究TSB分布相比于常见分布在度量金融风险方面的优势.实证结果表明,与正态分布、t分布、GED分布、双边Weibull分布和双边Lomax分布相比,基于该分布的GJR-GARCH模型具有最高的VaR预测精度.另外,文章将基于TSB分布的GJR-GARCH模型与Copula函数结合来构建均值-CVaR模型以研究多元投资组合的风险优化,实证研究亦表明能够刻画非对称特征的该模型具有更好的CVaR预测效果.最后,稳健性检验结果证实TSB分布对于金融风险预测以及投资组合优化的改进效果不依赖于波动率模型和Copula函数的设定.     

短期趋势判断与投资组合优选

针对股市非常有限的可预测性和投资组合优化时间窗口的选择问题,本文从股指趋势和个股收益率趋势类别两个层次上进行前瞻分析,并依据股指趋势判断和不同时间窗口对应的边际风险收益,提出投资组合优化计算的时间窗口选择规则,动态地进行资产组合优化。通过沪深A股及沪深300成份股两个样本集合的应用研究表明,考虑多层次短期趋势预测的动态投资组合选择方法能有效地改善资产组合绩效,是股市资产风险管理的有效方法之一。     

Studies on a general stock-bond integrated portfolio optimization model

The purpose of this paper is to extend a stock-bond integrated portfolio optimization model proposed by one of the authors in 1997 to the case where the universe covers risky (corporate) bonds in addition to stocks and risk-free (government) bonds. An integrated approach has been applied to Japanese market and was proved to generate a portfolio which usually outperforms standard asset allocation strategy. Inclusion of risky bonds is expected to lead to an even better portfolio. To properly handle risky bonds, we introduce a new scheme to quantify the risk associated risky bonds. We will demonstrate that the scheme proposed in this paper works very well, at least in the Japanese market.     

基于免疫记忆克隆算法的指数化投资组合优化构建策略

本文基于克隆选择学说及基于克隆选择学说及生物免疫响应过程的相关机理,提出用于指数化投资的免疫记忆克隆算法,并将其应用于指数化投资组合优化构建模型的求解,旨在探索指数化投资的优化构建策略。文章首先提出多目标的指数化投资组合构建模型。其次,分别设计了适用于指数化投资组合构建策略的抗原、抗体、亲和度函数、克隆选择算子、免疫记忆算子和相应的进化算法。该算法有效避免了传统遗传算法所存在的计算后期解的多样性差、易早熟以及收敛速度慢等缺点。同时,提出了限制投资组合中股票数量的启发式算法。最后,使用包括上证180指数在内的6组世界主要股票市场指数及其成份股的历史数据对模型及算法进行测算,结果表明算法具有良好的求解能力和收敛速度,所建模型的合理性和有效性亦被论证,模型和算法均具有很强的实践价值;     

基于引力搜索和粒子群混合优化算法的证券投资组合问题研究

本文研究考虑交易成本的投资组合模型,分别以风险价值(VAR)和夏普比率(SR)作为投资组合的风险评价指标和效益评价指标。为有效求解此模型,本文在引力搜索和粒子群算法的基础上提出了一种混合优化算法(IN-GSA-PSO),将粒子群算法的群体最佳位置和个体最佳位置与引力搜索算法的加速度算子有机结合,使混合优化算法充分发挥单一算法的开采能力和探索能力。通过对算法相关参数的合理设置,算法能够达到全局搜索和局部搜索的平衡,快速收敛到模型的最优解。本文选取上证50股2014年下半年126个交易日的数据,运用Matlab软件进行仿真实验,实验结果显示,考虑交易成本的投资组合模型可使投资者得到更高的收益率。研究同时表明,基于PSO和GSA的混合算法在求解投资组合模型时比单一算法具有更好的性能,能够得到满意的优化结果。     

不完全市场下考虑损失厌恶的连续时间投资组合选择

在不完全市场条件下研究了一般情形下的损失厌恶投资者的连续时间投资组合选择模型. 面对市场风险, 投资者的偏好由一个S-型的价值函数定义. 通过把不完全市场转换为完全市场, 利用鞅方法和复制技术, 分别获得了投资者的最优期末财富以及最优投资策略. 最后讨论了一个分段幂函数的例子, 在模型系数为确定的常数情形下, 得到了最优解的显示表达式.     

Portfolio Selection Problem with Minimax Type Risk Function

The investor's preference in risk estimation of portfolio selection problems is important as it influences investment strategies. In this paper a minimax risk criterion is considered. Specifically, the investor aims to restrict the standard deviation for each of the available stocks. The corresponding portfolio optimization problem is formulated as a linear program. Hence it can be implemented easily. A capital asset pricing model between the market portfolio and each individual return for this model is established using nonsmooth optimization methods. Some numerical examples are given to illustrate our approach for the risk estimation.     

Managing Cost Overrun Risk in Project Funding Allocation

This paper discusses decision making of project funding allocation under uncertain project costs. Because project costs are uncertain and funding allocations may not necessarily match the costs required, each project is inherently subject to a cost overrun risk (COR). In this paper, a model is proposed in which project cost is treated as a factor with a probability density function. The decision maker then allocates the total funding to the projects while minimizing a weighted sum of mean and variance of the COR of the project portfolio. Some properties of project COR are derived and interpreted. Optimal funding allocation, in relationship to factors such as various project sizes and riskiness, project interdependency, and the decision maker’s risk preference, is analyzed. The proposed funding allocation model can be integrated with project selection decision-making and provides a basis for more effective project control.     

Robust portfolio selection involving options under a “ marginal+joint ” ellipsoidal uncertainty set

In typical robust portfolio selection problems, one mainly finds portfolios with the worst-case return under a given uncertainty set, in which asset returns can be realized. A too large uncertainty set will lead to a too conservative robust portfolio. However, if the given uncertainty set is not large enough, the realized returns of resulting portfolios will be outside of the uncertainty set when an extreme event such as market crash or a large shock of asset returns occurs. The goal of this paper is to propose robust portfolio selection models under so-called “ marginal+joint” ellipsoidal uncertainty set and to test the performance of the proposed models. A robust portfolio selection model under a “marginal + joint” ellipsoidal uncertainty set is proposed at first. The model has the advantages of models under the separable uncertainty set and the joint ellipsoidal uncertainty set, and relaxes the requirements on the uncertainty set. Then, one more robust portfolio selection model with option protection is presented by combining options into the proposed robust portfolio selection model. Convex programming approximations with second-order cone and linear matrix inequalities constraints to both models are derived. The proposed robust portfolio selection model with options can hedge risks and generates robust portfolios with well wealth growth rate when an extreme event occurs. Tests on real data of the Chinese stock market and simulated options confirm the property of both the models. Test results show that (1) under the “ marginal+joint” uncertainty set, the wealth growth rate and diversification of robust portfolios generated from the first proposed robust portfolio model (without options) are better and greater than those generated from Goldfarb and Iyengar’s model, and (2) the robust portfolio selection model with options outperforms the robust portfolio selection model without options when some extreme event occurs.     

Financial portfolio management through the goal programming model: Current state-of-the-art

Since Markowitz (1952) formulated the portfolio selection problem, many researchers have developed models aggregating simultaneously several conflicting attributes such as: the return on investment, risk and liquidity. The portfolio manager generally seeks the best combination of stocks/assets that meets his/her investment objectives. The Goal Programming (GP) model is widely applied to finance and portfolio management. The aim of this paper is to present the different variants of the GP model that have been applied to the financial portfolio selection problem from the 1970s to nowadays.     

Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by ??-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiplepriors utility and the technique of backward stochastic differential equations (BSDEs), we transform the ??-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor??s uncertainty. Our model investigates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flexibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.