Tuesday, January 28th @ 11:00-12:30 PM (1011 Evans Hall)
A two-player price impact game
Moritz Voss, UCSB
ABSTRACT: We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank, Soner, Voss (2017), both facing common aggregated temporary and permanent price impact à la Almgren and Chriss (2001). 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. Preprint available