运用随机最优控制理论,建立了带有风险规避的证券投资最优策略问题的数学模型;然后,给出了值函数和风险规避系数的定义,并通过对值函数进行非线性变换,证明了变换后的值函数满足带有风险规避系数的HJB偏微分方程,特别当风险规避系数无限大时,给出了证券投资最优策略;最后给出了一个算例. By using the stochastic optimal control theory, a mathematic model of the optimal strategy for securities investment with risk aversion is established. Then, the definition of the value function and risk aversion coefficient is given. By nonlinear transformation of the value function, it is proved that The transformed value function satisfies the HJB partial differential equation with risk aversion coefficient, especially when the risk aversion coefficient is infinite, the optimal strategy of securities investment is given. Finally, an example is given.