效用函数意义下投资组合有效选择问题的研究

The Study on the Problem of Optimal Portfolio about Utility

我们知道 ,每个投资者在进行投资过程中 ,都有自己对收益与风险的偏好程度 ,即投资活动要遵循一个关于收益与风险的效用函数。按照古典经济学的分析 ,这个效用函数称为无差异曲线 (IDC) ,它是用均值 -方差来表现风险 -回报率相互替换的大小和形式的。每个投资者都拥有一条无差异曲线来表示他对于预期回报率和标准差的偏好。那么投资者如何确定他的一条无差异曲线 ,使他的最佳资产组合位于这条无差异曲线上 ?本文运用自己独创的一种几何方法解决了这个难题。本文首先把Markowitz模型的有效前沿用投资组合的权重向量表示出来 ,然后将无差异曲线也用抽资组合的权重向量表示出来 ,再由资产组合的有效选择原则就求出这个无差异曲线了。

As known as well,every investor has his preferences for risk and return in his investing activity.In other words,every investor's activity should abide by an utility of risk-return.Following classical economic analysis,an utility function is called an indifference curve(IDC),and it is developed showing the magnitude and form of the risk-return trade-off in a mean-variance framework.Every investor has a family of indifference curves to represent his preferences for risk and return.How do an investor decide an IDC on which his optimal portfolio lie?In this paper,we solve this problem by applying a geometric method.First,we denote the efficient frontier of Markowitz model with the weights vector of portfolio.Second,we denote the IDCs with the weights vector of portfolio.By the rule of efficient selection of portfolio,we're thus able to find this IDC.