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

European Journal of Operational Research, 2019

31 Pages Posted: 6 Apr 2017 Last revised: 29 Sep 2019

See all articles by Pavol Brunovsky

Pavol Brunovsky

Comenius University - Faculty of Mathematics, Physics and Informatics

Aleš Černý

Cass Business School, City, University of London

Ján Komadel

Comenius University - Faculty of Mathematics, Physics and Informatics

Date Written: April 5, 2017

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; Tóth 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.

Keywords: optimal liquidation, price impact, square-root law, singular boundary value problem, stochastic optimal control

JEL Classification: G11, G12

Suggested Citation

Brunovsky, Pavol and Černý, Aleš and Komadel, Ján, Optimal Trade Execution Under Endogenous Pressure to Liquidate: Theory and Numerical Solutions (April 5, 2017). European Journal of Operational Research, 2019. Available at SSRN: https://ssrn.com/abstract=2946755 or http://dx.doi.org/10.2139/ssrn.2946755

Pavol Brunovsky

Comenius University - Faculty of Mathematics, Physics and Informatics ( email )

Mlynská dolina
SK-842 48 Bratislava, 842 48
Slovakia

Aleš Černý (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Ján Komadel

Comenius University - Faculty of Mathematics, Physics and Informatics ( email )

Mlynská dolina
SK-842 48 Bratislava, 842 48
Slovakia

Register to save articles to
your library

Register

Paper statistics

Downloads
36
Abstract Views
284
PlumX Metrics