机会约束下的投资组合问题

不同的投资者会有不同的期望收益率与置信水平，因此就会采取不同的投资策略，在证券收益率服从正态分布的前提下，提出了在允许卖空时的一类机会约束下的投资组合问题，它是以期望收益与置信水平为导向的，建立了其数学模型，讨论了最优解的存在性与唯一性，得到了最优解的解析表达式，并利用Matlab语言给出了求解有效边界曲线，可行集，机会约束问题的最优解，最优解的均值以及标准差的程序，最后举例予以了说明。

Chance-constrained portfolio problem

Different investors had different expected rates of return and different confidence levels, so they would make different investment decisions. When securities rates of return obeyed normal distribution, a chance-constrained portfolio problem with short selling, which was determined by expected rate of return and confidence level, was put forward. Its mathematical model was established, and the properties of existence and uniqueness of the optimal solution were discussed. Furthermore, the explicit representation of the optimal solution is given. By Matlab language, the program of obtaining efficient frontier, permission set, mean and standard deviation of the optimal solution is devised. Finally, an illustrative example is provided.