Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions |
| |
Authors: | Pavol Brunovský Aleš Černý Ján Komadel |
| |
Institution: | 1. Department of Applied Mathematics and Statistics, Comenius University Bratislava, Bratislava 84248, Slovakia;2. Cass Business School, City, University of London, 106 Bunhill Row, London EC1Y 8TZ, UK |
| |
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 & Rakhlin,2013; Farmer et?al., 2013; Donier et?al., 2015; Tóth (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 |
本文献已被 ScienceDirect 等数据库收录! |
|