具有随机特征的风险投资组合问题分析

利用随机微分方程理论,对一类具有随机特征的风险投资组合问题进行深入研究.通过选择适当的效用函数,在假设最优投资组合方案存在的情况下,结合随机最优控制中的Hamilton-Jacobi-Beuman方程,建立相应的拉格朗日函数,得到具有随机特征的风险投资组合问题最优投资策略的一个定量结果.并在定量研究的基础上进行定性分析,得到与风险投资理论相吻合的结论.

Research on a Risk Investment Portfolio with Stochastic Character

With the theory of stochastic differential equation, the authors discuss a problem of a class of risk investment portfolio with stochastic character. With the selection of appropriate utility function and combines the Hamilton-Jacobi-Bellman equation, under the assumption that an optimal portfolio exists, and by using the Homologous Lagrangian function, some quantitative results of this risk optimal investment portfolio are given. With these quantitative results, some qualitative results are got. These results concord with the results of the theory of risk investment.