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.     

幂式亚期权的定价方法

幂期权和亚期权是两种新型期权,而幂式亚期权是二者的统一.由幂期权和亚期权概念引出幂式亚期权定义,对连续时间的几何平均型幂式亚期权的定价公式进行了推导,并得到了其解析解.     

线性增长的半连续函数的逼近定理

证明了定义在R上的上（下）半连续函数.若满足线性增长条件,则可由满足李普希茨条件的连续函数序列从上（下）方逼近.推广了闭区间上的半连续函数的逼近定理.     

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。     

非线性数学期望的收敛定理

从非线性数学期望的定义及其性质入手，通过与经典数学期望的比较，并利用经典的Lebesgue收敛定理和倒向随机微分方程解在L^2意义下的连续性，提出并证明了被P控制的非线性数学期望的Levi，Fatou及Lebesgue收敛定理，从而得到在适当条件下非线性数学期望在几乎处处意义下连续；同时指出这些结果对任意一个g-期望都成立．