Optimal solution of the liquidation problem under execution and price impact risks

Francesca Mariani and Lorella Fatone

Quantitative Finance, 2022, vol. 22, issue 6, 1037-1049

Abstract: We consider an investor that trades continuously and wants to liquidate an initial asset position within a prescribed time interval. As a consequence of his trading activity, during the execution of the liquidation order, the investor has no guarantees that the placed order is executed immediately; it may go unfilled, partially filled or filled in excess. The uncertainty in the execution affects the trading activity of the investor and the asset share price dynamics generating additional sources of noise: the execution risk and the price impact risk, respectively. Assuming the two sources of noise correlated and driven by the cumulative effect of the investor trading strategy, we study the problem of finding the optimal liquidation strategy adopted by the investor in order to maximize the expected revenue resulting from the liquidation. The mathematical model of the liquidation problem presented here extends the model of Almgren and Chriss [Optimal execution of portfolio transactions. J. Risk, 2000, 3(2), 5–39] to include execution and price impact risks. The liquidation problem is modeled as a linear quadratic stochastic optimal control problem with the finite horizon and, under some assumptions about the functional form for the magnitude of execution and price impact risks, is solved explicitly. The derived solution coincides with the optimal trading strategy obtained in the absence of execution uncertainty for an asset price with a modified growth rate. This suggests that the uncertainty in the execution modifies the directional view of the investor about the future growth rate of the asset price.

Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1080/14697688.2022.2047219 (text/html)
Access to full text is restricted to subscribers.

Related works:
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:taf:quantf:v:22:y:2022:i:6:p:1037-1049

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RQUF20

DOI: 10.1080/14697688.2022.2047219

Access Statistics for this article

Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral

More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().