证券投资风险最优控制问题

在假设证券价格服从几何布朗运动的基础上·首先,建立了证券投资决策最优控制问题数学模型,并把经济学家提出的风险规避系数概念引入到证券投资决策问题中·然后,根据随机最优控制理论,推导出了风险规避投资者的值函数所满足的带有风险规避系数的动态规划偏微分方程,并且得到了基于随机最优控制问题值函数的证券投资最优策略·特别,当风险规避系数无限大时,得到了风险规避投资者的最优投资策略,最后,给出一个算例·

Risk Optimal Control for Security Investment

An optimal control model for the security investment decision was established based on the assumption that the security price follows the geometric Brownian Motion. The conception of risk aversion coefficient proposed by economists was introduced into the model for security investment decision. Dynamic programming partial differential equation with the coefficient of risk aversion was obtained on the basis of the stochastic control theory. The equation can meet the value of the risk aversion investor. The security investment optimal tactics was set up based on the value function of the stochastic optimal control. Particularly,the security investment optimal tactics for the investor of risk aversion was also found out for the infinite coefficient of risk aversion. An example was provided.