Before revision: We solve  the optimal trade execution problem in the Almgren and Chirss framework with the Value-at-risk / Expected Shortfall based criterion of Gatheral and Schied when the underlying unaffected stock price follows a displaced diffusion model. 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.
After revision: We solve the optimal trade execution problem in the Almgren and Chirss framework with the Value-at-risk / Expected Shortfall based criterion of Gatheral and Schied when the underlying unaffected stock 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 a geometric Browinan motion (GBM) type dynamics may prevail, thus serving as a bridge between the ABM and GBM frameworks.