General Intensity Shapes in Optimal Liquidation

39 Pages Posted: 5 Jun 2015

See all articles by Olivier Edmond Guéant

Olivier Edmond Guéant

Université Paris VII Denis Diderot

Charles‐Albert Lehalle

Capital Fund Management

Date Written: July 2015

Abstract

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.

Keywords: optimal liquidation, limit orders, stochastic optimal control, viscosity solutions

Suggested Citation

Guéant, Olivier Edmond and Lehalle, Charles‐Albert, General Intensity Shapes in Optimal Liquidation (July 2015). Mathematical Finance, Vol. 25, Issue 3, pp. 457-495, 2015. Available at SSRN: https://ssrn.com/abstract=2614740 or http://dx.doi.org/10.1111/mafi.12052

Olivier Edmond Guéant (Contact Author)

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Charles‐Albert Lehalle

Capital Fund Management

23 rue de l'Université
Paris, 75007
France

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