Trading with the Crowd

52 Pages Posted: 29 Jun 2021

See all articles by Eyal Neuman

Eyal Neuman

Imperial College London - Department of Mathematics

Moritz Voss

Technische Universität Berlin (TU Berlin)

Date Written: June 17, 2021

Abstract

We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with taking into account a common general price predicting signal. The unique Nash-equilibrium strategies reveal how each agent's liquidation policy adjusts the predictive trading signal to the aggregated transient price impact induced by all other agents. This unfolds a quantitative relation between trading signals and the order flow in crowded markets. We also formulate and solve the corresponding mean field game in the limit of infinitely many agents. We prove that the equilibrium trading speed and the value function of an agent in the finite $N$-player game converges to the corresponding trading speed and value function in the mean field game at rate $O(N^{-2})$. In addition, we prove that the mean field optimal strategy provides an approximate Nash-equilibrium for the finite-player game.

Keywords: Crowding, Optimal Portfolio Liquidation, Price Impact, Mean Field Games, Optimal Stochastic Control, Predictive Signals

JEL Classification: C73, C02, C61, G11

Suggested Citation

Neuman, Eyal and Voss, Moritz, Trading with the Crowd (June 17, 2021). Available at SSRN: https://ssrn.com/abstract=3868708 or http://dx.doi.org/10.2139/ssrn.3868708

Eyal Neuman (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Moritz Voss

Technische Universität Berlin (TU Berlin) ( email )

Straße des 17
Juni 135
Berlin, 10623
Germany

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