Optimal Trade Execution Under Endogenous Pressure to Liquidate: Theory and Numerical Solutions

Pavol Brunovsk\'y, Ale\v{s} \v{C}ern\'y and J\'an Komadel
Authors registered in the RePEc Author Service: Aleš Černý

Papers from arXiv.org

Abstract: We study optimal liquidation of a trading position (so-called block order or meta-order) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the unaffected asset price while simultaneously ruling out short sales. In this setting the liquidation time horizon becomes a stopping time determined endogenously, as part of the optimal strategy. We find that the optimal liquidation strategy is consistent with the square-root law which states that the average price impact per share is proportional to the square root of the size of the meta-order (Bershova and Rakhlin, 2013; Farmer et al., 2013; Donier et al., 2015; T\'oth et al., 2016). Mathematically, the Hamilton-Jacobi-Bellman equation of our optimization leads to a severely singular and numerically unstable ordinary differential equation initial value problem. We provide careful analysis of related singular mixed boundary value problems and devise a numerically stable computation strategy by re-introducing time dimension into an otherwise time-homogeneous task.

Date: 2017-07
New Economics Papers: this item is included in nep-mst
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in European Journal of Operational Research, 264(3), 1159-1171, 2018

Downloads: (external link)
http://arxiv.org/pdf/1707.07284 Latest version (application/pdf)

Related works:
Journal Article: Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions (2018)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1707.07284

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().