变点CAViaR市场风险测量模型及创业板应用

提出了带有结构变点的条件分位数自回归模型,借助于不对称拉普拉斯分布,给出了基于贝叶斯推理和马尔科夫链蒙特卡罗模拟抽样的参数估计方法.通过(无、单、双)变点间接GARCH方程(IG)模型与对称绝对值方程(SAV)模型的比较以及风险值预测效果统计检验,发现单变点SAV模型是预测我国创业板指数市场风险的最优模型,且变点的估计均值紧邻首次限售解禁日期;证实了首次限售股解禁引起的原始股大量减持和频繁的高管离职是市场风险演化模式结构变化的主要成因,且变点后的市场风险平均水平以及滞后消息对风险的冲击强度均低于变点前的水平,因此必须加强对高管减持行为的监管,以保护中小投资者利益.     

非负随机矩阵Kronecker积的谱半径的不等式

给出了随机矩阵的Kronecker积的元素的表达式,通过表达式研究了非负随机矩阵的Kronecker积的数学期望的性质,建立了随机矩阵的Kronecker积的数学期望与随机矩阵的数学期望的Kronecker积的元素之间的关系不等式．选择了一个合适的矩阵范数,将矩阵的谱半径表示成矩阵范数的极限形式．在此基础上,利用数学期望的性质和Kronecker积的性质证明了非负随机矩阵的Kronecker积的谱半径的几个不等式,其中包括矩阵函数不等式、分块矩阵不等式;通过实例说明了主要结果在非线性时间序列模型中的应用．     

Research on Efficient Frontier of Portfolios with Transaction Cost

This paper is concerned with a study on the efficient frontier characters of portfolio with transaction cost. The conclusion is drawn that all portfolios are of positive correlation on the efficient frontier with transaction cost; the sufficient condition for the derivable efficient frontier has also been achieved. Meanwhile, in comparison with the position of the efficient frontier without transaction cost in the plane (σ2,R), the conclusion has been made that the efficient frontiers with transaction cost drift and its opening shrinks correspondingly. With this study, the content of the efficient frontier is further enriched. It's very constructive and important for the practical portfolio investment strategy.     

Research on Efficient Frontier of Portfolios with Transaction Cost

This paper is concerned with a study on the efficient frontier characters of portfolio with transaction cost.The conclusion is drawn that all portfolios are of positive correlation on the efficient frontier with transaction cost;the sufficient condition for the derivable efficient frontier has also been achieved. Meanwhile, in comparison with the position of the efficient frontier without transaction cost in the plane (σ^2,R) , the conclusion has been made that the efficient frontiers with transaction cost drift and its opening shrinks correspondingly. With this study, the content of the efficient frontier is further enriched. It‘s very constructive and important for the practical portfolio investment strategy.     

证券数减少情形下M-V证券组合特征灵敏度研究

基于均值-方差（M—V）投资组合选择模型，分析了证券市场上不存在无风险资产且允许卖空条件下证券组合特征关于证券数减少的灵敏度．通过引入扰动因子和扰动矩阵，建立了证券数减少时M—V组合模型．同时与原有模型进行了比较，分析了证券数减少对有效前沿的影响．结果表明：证券数减少时M—V证券组合有效前沿向右漂移且开口变大，并给出了相应的经济解释．     

基于双层规划的投资组合选择模型研究

基于均值-方差投资组合选择模型,分析了市场上不存在无风险资产条件下的一类双层规划的投资组合选择问题.针对投资组合问题中参数估计不确定情形,引入了区间来描述期望收益率.通过将该问题转化为标准的极大极小问题,并借助Lagrange乘子法,得到了模型的最优投资策略和有效前沿的解析表达式.利用上海证券市场交易数据,结合数值算例分析验证了该模型在投资实践中的可行性和有效性.     

随机变量若干性质的研究

对随机变量的几个重要的性质进行了研究。