在Black-Scholes型金融市场下,研究了三种安全第一准则意义下的动态投资组合问题,利用非线性规划理论,给出了最优投资策略的显式表达式。结果表明最优投资策略符合两基金定理,即由无风险资产和市场组合构成。并结合数值例子,在均值-方差框架下分析了三种准则的联系和经济意义。 Under the Black-Scholes financial market, the dynamic investment portfolio under three safety first criteria is studied. By using the theory of nonlinear programming, the explicit expression of the optimal investment strategy is given. The result shows that the optimal investment strategy conforms to the two-fund theorem, which consists of risk-free assets and market portfolio. Combined with the numerical examples, the connection and economic significance of the three criteria are analyzed under the mean-variance framework.