General intensity shapes in optimal liquidation

The classical literature on optimal liquidation, rooted in Almgren-Chriss models, tackles the optimal liquidation problem using a trade-off between market impact and price risk. It answers the general question of optimal scheduling but the very question of the actual way to proceed with liquidation is rarely dealt with. Our model, which incorporates both price risk and nonexecution risk, is an attempt to tackle this question using limit orders. The very general framework we propose to model liquidation with limit orders generalizes existing ones in two ways. We consider a risk-averse agent, whereas the model of Bayraktar and Ludkovski only tackles the case of a risk-neutral one. We consider very general functional forms for the execution process intensity, whereas Guéant, Lehalle and Fernandez-Tapia are restricted to exponential intensity. Eventually, we link the execution cost function of Almgren-Chriss models to the intensity function in our model, providing then a way to see Almgren-Chriss models as a limit of ours.