Time consistent in efficiency dynamic mean-variance policy

The dynamic mean-variance formulation for a market with all risky assets is not time consistent in efficiency (TCIE), in the sense that the pre-committed policy, which is optimal for the entire investment horizon, could become mean-variance inefficient when facing a truncated time-horizon problem at an intermediate time instant. By removing the self-financing restriction and fully avoiding the irrational investment behaviours in intermediate time periods, we develop the TCIE dynamic mean-variance policy, which is TCIE. Comparing to the polices in the literature, such as the strictly dominating policy, the pre-committed policy and the time consistent policy, the TCIE policy can achieve better global investment performance.