带有初始风险证券的最优组合投资

Portfolio optimization with original risk stocks

对带有初始风险证券的投资者如何进行投资以及当风险证券的收益率或者风险发生变化时如何调整投资策略的问题进行了研究.以最大最小化平均绝对离差作为风险测度建立模型,求解模型得到最优投资策略.着重讨论了当风险证券的收益率或风险发生变化时,最优投资策略的稳定性以及最优投资策略的调整.得到了当某个风险证券的收益率或其风险发生变化时,最优投资策略的稳定条件以及策略的调整方案.还刻画了有效边界的结构,并证明了有效边界是一条折线段.最后对含无风险证券的情形进行了讨论并得到了相应结论.

This paper studies how an investor with original risk stocks invests and how he adjusts his investment policies when the mean return rate or risk of some stock varies. With the minimax meanabsolute deviation as risk measure, we set up the model and obtain the optimal investment policies. In particular, we discuss the stability and the adjustment of the optimal policies when the mean return rate or risk of some stock varies. The stable conditions for the optimal policies and the methods of adjustment are obtained. Also we characterize the structure of the efficient frontier and show that the efficient frontier is continuous and piecewise linear. Finally, we discuss the case where there exists a riskless asset and obtain corresponding results.