风险投资中三类经典优化模型等价性分析

风险投资中有三类经典优化模型，分别是风险极小化模型、期望收益极大化模型、风险厌恶模型。这三类模型的等价会为投资组合分析提供更多的方法。文中证明了三类优化模型产生相同的有效前沿，并在此意义下得出这三类优化模型的等价性。另外，引用MSCI世界股价指数数据对三个模型有效前沿的等价性，进行实际算例验证。

The equivalency analysis of three classical optimization models in risk investment

The three classical optimization models in risk investment are risk minimization model, expected revenue maximization model and Risk aversion model. The equivalency of these three classical optimization models will provide more approaches in future risk investment analysis. It is proved in this paper that the three optimization models produce the same effective frontiers, and in this sense, it is concluded that the three classical optimization models are equivalent. In addition, the numerical example is presented with reference to the MSCI World Stock Index data to explain the equivalency of the three models.