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.