  We solve a version of the optimal trade execution problem when the mid asset
price follows a displaced diffusion. Optimal strategies in the adapted class
under various risk criteria, namely value-at-risk, expected shortfall and a new
criterion called "squared asset expectation" (SAE), related to a version of the
cost variance measure, are derived and compared. It is well known that
displaced diffusions (DD) exhibit dynamics which are in-between arithmetic
Brownian motions (ABM) and geometric Brownian motions (GBM) depending of the
choice of the shift parameter. Furthermore, DD allows for changes in the
support of the mid asset price distribution, allowing one to include a minimum
permitted value for the mid price, either positive or negative. We 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 differences are not negligible for high levels of risk aversion and
low market impact assets. This is illustrated with numerical examples.
