We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies  under various risk criteria, namely value-at-risk, expected shortfall and a  version of the cost variance measure  are derived and compared. It is well known that displaced diffusions  exhibit dynamics which are in-between arithmetic Brownian motions (ABM) or geometric Brownian motions (GBM) depending of the choice of the shift parameter. The model presented in the paper attempts to provide 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  .
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 .
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in the adapted class
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new criterion called "squared asset expectation" (SAE), related to a
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,
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(DD)
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or
and
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The model presented in the paper attempts to provide a bridge between the approach of Almgren and Chris (ABM) and Gatheral and Schied (GBM) to optimal execution. We also
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
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the difference
differences
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. This is illustrated with numerical examples