Before revision:  We also show that the difference in terms of liquidity premiumbetween the constant participation rate case and the usual Almgren-Chriss-like case never exceeds 15\% .
After revision:  We also provide a thorough comparison between IS strategies and POV strategies in terms of liquidity premiumbetween the constant participation rate case and the usual Almgren-Chriss-like case never exceeds 15\% .