Assuming a particular price process, it was shown by Gatheral that a model that combines nonlinear price impact with exponential decay of market impact admits price manipulation, an undesirable feature that should lead to rejection of the model. Subsequently, Alfonsi and Schied proved that their...

In this review article, we present recent work on the regularity of dynamical market impact models and their associated optimal order execution strategies. In particular, we address the question of the stability and existence of optimal strategies, showing that in a large class of models, there...

We consider the linear-impact case in the continuous-time market impact model with transient price impact proposed by Gatheral (2008). In this model, the absence of price manipulation in the sense of Huberman and Stanzl (2004) can easily be characterized by means of Bochner's theorem. This...

Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling. A recent paper by Maccheroni et al. (2004) characterizes investor preferences under aversion against both risk and ambiguity. Their result shows that these preferences can be numerically represented in...