Before revision: The risk minimizing problem E[l((H-X_T^{x,\pi})^{+})]\pi{\longrightarrow}\min in the  Black-Scholes framework with correlation is studied.
After revision: The risk minimizing problem E[l((H-X_T^{x,\pi})^{+})]\pi{\longrightarrow}\min in the multidimensional Black-Scholes framework with correlation is studied.