Before revision:  For a multiple-security case, we use an interesting connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties have been studied by Bismut(1976)  .
After revision:  For a multiple-security case, we use an interesting connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties have been studied by Bismut(1976) . We also propose a perturbative approximation scheme for the resultant BSRDE, which only requires a system of linear ODEs to be solved at each expansion order. Its justification and the convergence rate are also given .