损失极小的证券投资组合

Security Investment of Only A Few Loss

投资者往往采用组合证券投资方式以分散风险,并取得适当的投资收益.该文在分析风险损失的基础上,提出一种新的证券投资组合模型,并着重运用随机最优控制求解.根据值函数和风险规避系数的定义,说明经非线性变换后的值函数满足带有风险规避系数的HJB偏微分方程.当风险规避系数无限大时,给出了证券投资最优策略.最后给出一个算例,表明带有规避系数的HJB偏微分方程可得值函数和相应的投资策略.

A model of portfolio selection is developed on the basis of the definition of loss,with focus on its resolution by means of the theory of stochastic optimal control.Based on the definition of the value function and the coefficient of risk aversion, the nonlinear transformation of value function was proved to be in agreement with HJB partial differential equation with the coefficient of risk aversion. Security investment tactics was proposed on the condition that the coefficient of risk aversion is infinite.Then the problem was further discussed with an example.