Before revision:  The displaced diffusion model can conveniently model at the same time situations where either an arithmetic Brownian motion (ABM) or a geometric Browinan motion (GBM) type dynamics may prevail, thus serving as a bridge between the ABM and GBM frameworks. We introduce alternative risk criteria and we notice that the optimal trade executionstrategy little depends on the specific risk criterion we adopt. In most situations the solution is close to the simple Volume Weighted Average Price (VWAP) solution regardless of the specific diffusion dynamics or risk criterion that is chosen, especially on realistic trading horizons of a few days or hours. This suggests that more general dynamics need to be considered, and possibly more extreme risk criteria, in order to find a relevant impact on the optimal strategy
After revision:  The displaced diffusion model can conveniently model at the same time situations where either an arithmetic Brownian motion (ABM) or a geometric Browinan motion (GBM) type dynamics may prevail, thus serving as a bridge between the approach of Almgren and Chris (ABM) and Gatheral and Schied (GBM) to optimal execution. We also study the dependence of the optimal solution on the choice of the risk aversion criterion. Optimal solutions across criteria and asset dynamics are comparable although the difference are not negligible for high levels of risk aversion and low market impact assets.