A two-player portfolio tracking game

Abstract

We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank et al. [5], both facing common aggregated temporary and permanent price impact à la Almgren and Chriss [2]. The resulting stochastic linear quadratic differential game with terminal state constraints allows for an explicitly available open-loop Nash equilibrium in feedback form. Our results reveal how the equilibrium strategies of the two players take into account the other agent's trading targets: either in an exploitative intent or by providing liquidity to the competitor, depending on the ratio between temporary and permanent price impact. As a consequence, different behavioral patterns can emerge as optimal in equilibrium. These insights complement existing studies in the literature on predatory trading models examined in the context of optimal portfolio liquidation problems.

Portfolio liquidation games with self‐exciting order flow

“…We allow all impact parameters and cost coefficients to be stochastic. Liquidation games with instantaneous and permanent impact and with and without strict liquidation constraint have been studied in Carlin et al (2007); Drapeau et al (2021); Evangelista and Thamsten (2020); Fu and Horst (2020); Voß (2019). Although our mathematical framework would clearly be flexible enough to allow for an additional permanent impact we deliberately choose not to include a permanent impact as it does not alter the mathematical analysis.…”

Portfolio Liquidation Games with Self-Exciting Order Flow

“…We allow all impact parameters and cost coefficients to be stochastic. Liquidation games with instantaneous and permanent impact and with and without strict liquidation constraint have been studied in [12,18,20,23,45]. Although our mathematical framework would clearly be flexible enough to allow for an additional permanent impact we deliberately choose not to include a permanent impact as it does not alter the mathematical analysis.…”