We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs’ optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain around the continuous-time limit. Unlike in the risk-neutral case, the optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large. In contrast, the HFTs’ risk-adjusted profits and the equilibrium price impact converge to their risk-neutral counterparts. Compared to a social-planner solution for cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity. (Joint work with Johannes Muhle-Karbe, Dapeng Shang, and Chen Yang.)

Dr. Sebastian Herrmann is  currently a Byrne Research Assistant Professor in the University of Michigan Department of Mathematics.  He received his PhD in Mathematics from ETH Zurich in 2016 in the area of probability and stochastic processes.