Trading against disorderly liquidation of a large position under asymmetric information and market impact

¹ CREST, Ensae, Université Paris Saclay, 3 av Pierre Larousse, 92245 Malakoff, France
² Department of Mathematics and Statistics, Concordia University, 1455 Boulevard de Maisonneuve Ouest, Montréal, QC H3G 1M8, Canada
³ ISFA, Université Lyon 1, 50 avenue Tony Garnier, 69007 Lyon, France

^a E-mail: caroline.hillairet@ensae.fr
^b E-mail: cody.hyndman@concordia.ca
^c E-mail: renjie.wang@concordia.ca
^d E-mail: ying.jiao@univ-lyon1.fr

Abstract

We consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold. Liquidation occurs in a disorderly manner and negatively impacts the market price of the asset. We consider the perspective of small investors whose trades do not induce market impact and who possess different levels of information about the liquidation trigger mechanism and the market impact. We classify these market participants into three types: fully informed, partially informed and uninformed investors. We consider the portfolio optimization problems and compare the optimal trading and wealth processes for the three classes of investors theoretically and by numerical illustrations.