不允许卖空证券组合选择的有效子集

证券组合选择的有效子集是指它可取代原有的基本证券集来生成Markowits有效组合前沿.本文给出一个证券集的子集在不允许卖空的条件下是全集的有效子集的充要条件。     

证券集的组合前沿分类与有效子集

本文通过引入证券价格 ,讨论一般证券集组合前沿的分类 ,并据此直接证明判定某个证券子集是全集的有效子集的一个充要条件     

奇异协方差阵下证券组合的有效子集

Szeg\"{o}曾猜想当协方差阵奇异时可能存在有效子集, 本文在奇异协方差阵下利用有效组合的通解, 给出了证券组合有效子集的一个等价定义, 并得到了在证券全集中存在有效子集的充要条件,还给出了证券子集为有效子集的一些新的充要条件.     

证券组合选择有效子集的分类与搜索方法

本文在对证券组合选择有效子集的分类基础上,给出一个证券组合选择有效子集的搜索方法-逐个别法,并证明了它的有效性.     

证券数目变化时受到扰动的M-V有效前沿分析

基于M-V证券组合模型,在证券市场上不存在无风险资产且允许卖空条件下,探讨了证券数增加k种后原n种证券协方差矩阵发生改变情形下M-V证券组合有效前沿的漂移问题。通过引入扰动因子和扰动矩阵,给出了M-V证券组合有效前沿的漂移方向及其开口大小的变化情况．研究结果表明证券数增加了k种后有效前沿向左漂移以及它的开口变大,原证券组合的有效前沿完全落在新的证券组合可行集内．     

奇异协方差阵下有效前沿及有效组合的解析解

利用广义逆矩阵研究了协方差阵奇异时的投资组合问题,突破了传统方法中要求协方差阵可逆的限制,得到了证券市场存在有效组合的充要条件,并给出了有效前沿和有效组合的解析解,成功地推广了经典Markowitz模型,同时还将有助于证券组合有效子集的深入研究.     

具指数赋权指标的证券投资多目标线性规划模型

本文提出证券投资决策的指数赋权指标体系．在该指标体系中,建立风险证券组合投资决策和存在无风险证券或无风险贷款时证券组合投资决策的多目标线性规划模型．研究了有效风险证券组合集和有效证券组合集的结构和相互关系,市场证券组合以及证券均衡市场价格和投资风险分析．     

最小方差组合证券集的性质

从分析最小方差组合证券集入手 ,研究了均值方差有效组合证券边界的性质 ,给出最小方差组合证券集是一个仿射集 ,并且对有效组合证券结构的统计特性进行了分析 ,对证券投资有一定的指导意义     

一般M-V模型中的有效证券组合及无套利分析

本文研究了协方差阵奇异时一般M-V模型中的有效证券组合, 得到了证券市场存在有效证券组合的充要条件, 并给出了有效证券组合的通解和有效前沿的性质. 最后, 本文还在奇异协方差阵下进行了无套利分析, 得到了证券市场无套利的充要条件, 从而证明了Szeg\"{o}的猜想.     

证券组合M-V有效前沿旋移分析的进一步研究

在市场上存在无风险资产且允许卖空的条件下,研究了新增加k种证券后对原有效前沿的影响.引入了有效证券和无效证券,给出了M-V证券组合有效前沿旋移的方向.研究结果表明新增加证券后有效前沿的斜率变大.     

基于基准过程的动态均值-方差最优投资组合选择

利用动态规划方法研究了基于基准过程的动态均值-方差最优投资组合问题,证明了识别定理,得到了剩余过程的均方最优投资策略和有效前沿.     

证券数增加情形下证券组合有效边缘特征灵敏度分析

本文较为详细地讨论了当证券市场不存在无风险收益证券且允许卖空时证券数的增加对 M-V证券组合有效边缘及其特征的影响 ,给出了有效边缘、渐近线斜率、全局最小方差证券组合及其协方差、最小方差证券组合的投资权数等的变化模式     

t-分布与不同风险度量下有效投资组合及其边缘的相互关系研究

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASUREgS

In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.