Before revision:  It is proved that all the contingent claims in this model are attainable in the sense of Xiong and Zhou. Further, we propose a numerical scheme to approximate the optimal portfolio  .
After revision:  It is proved that all the contingent claims in this model are attainable in the market model is complete even in this case while the information is not complete and the drift is uncertain. Then, the optimal strategy based on partial information is derived, which reduces to solving a related backward stochastic differential equation (BSDE). Finally, we propose an efficient numerical scheme to approximate the optimal portfolio .