Dynamic Revised Mean-Variance Policy in a Market without Riskless Asset

Due to the nonseparable variance term, the dynamic mean-variance portfolio selection in market without riskless asset is not time consistent or time consistent in efficiency. Similar to the market with riskless asset, the investor can perform as good as the truncated global optimal mean-variance policy with revised lower funding level. Thus, we propose a dynamic revised mean-variance policy, which is better than the global optimal policy.