有交易费的证券组合投资模型研究

【作者】 李科学；

【导师】 师义民；

【作者基本信息】 西北工业大学 ， 应用数学， 2004， 硕士

【摘要】 证券组合投资是当今金融界研究的热点之一，受到了国内外许多学者的重视，已有许多研究成果。但绝大部分研究结论都未考虑证券投资的交易费。而在实际中，交易费是不可避免的。没有交易费的证券投资将导致证券市场的无序。忽略交易费将导致证券投资组合方案失去应用价值。交易费是指投资者在证券投资中需要交纳一定的费用，证券交易费包括交给国家的印花税和交给券商的佣金等。 本文研究了含有交易费用的证券组合投资模型。主要工作有： 1．在证券收益率之间的协方差阵为正定矩阵时，给出了以β值风险为风险指标的含有交易费的证券组合投资模型，并分别在允许卖空和不允许卖空两种情形下进行了讨论。 2．在证券收益率之间的协方差阵为非负定矩阵时，给出了以收益率方差为风险指标的含有交易费的证券组合模型，分别在允许卖空和不允许卖空两种情形下进行了讨论。 3．在证券收益率协方差阵不一定存在时，给出了不同于以往以证券收益率间的方差或是半方差为风险度量指标而是以绝对离差为风险指标和以半绝对离差为风险指标的含有交易费用的证券组合投资模型。 4．在理想状态下，即投资者可以支配的资金为充分大的情况下，将交易费函数近似线性化，研究了含有交易费的证券组合投资模型。更多还原

【Abstract】 Nowdays, the portfolio investment is becoming one of financial hotspots. But most research results are gained without transaction costs . Transaction costs can’t be parried from investment research. In practice, investor will get invalid portfolio without taking into account transaction costs. Without transaction costs, portfolio will be out of effect.Transaction costs is that investor need to hand in when he invest, it contains printing costs (investor hands it to country) and commission (investor hands it to bourse)The paper focuses on research about portfolio model with transaction costs. When the covariance matrix formed by securities yields is positive definite ,we provide the model with transaction costs, the risk is B index risk, researching the model under short sale and no short sale separately. When the covariance matrix formed by securities yields is non-oppositive definite , we provide the model with transaction costs, which risk is variance matrix risk .When the covariance matrix formed by securities yields is not exist, the risk we use is absolute deviation risk and semi-absolute deviation, which is differ with traditional risk such as variance matrix risk or semi- variance matrix risk. At last we provide the model with transaction costs with a view to the capital is large enough .We linearize transaction costs function to linear function, then we research the model.更多还原