Comparison between the Mean Variance optimal and the Mean

5 We compare optimal liquidation policies in continuous time in the presence of trading impact using 6 numerical solutions of Hamilton Jacobi Bellman (HJB) partial differential equations (PDE). In par7 ticular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent 8 (pre-commitment) mean-variance strategy. We show that the two different risk measures lead to very dif9 ferent strategies and liquidation profiles. In terms of the optimal trading velocities, the mean-quadratic10 variation strategy is much less sensitive to changes in asset price and varies more smoothly. In terms 11 of the liquidation profiles, the mean-variance strategy strategy is much more variable, although the 12 mean liquidation profiles for the two strategies are surprisingly similar. On a numerical note, we show 13 that using an interpolation scheme along a parametric curve in conjunction with the semi-Lagrangian 14 method results in significantly better accuracy than standard axis-aligned linear interpolation. We also 15 demonstrate how a scaled computational grid can improve solution accuracy. 16