Trading with the crowd
File(s)
Author(s)
Neumann, Eyal
Voss, Moritz
Type
Journal Article
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.
Date Issued
2023-07
Date Acceptance
2023-03-22
Citation
Mathematical Finance, 2023, 33 (3), pp.548-617
ISSN
0960-1627
Publisher
Wiley
Start Page
548
End Page
617
Journal / Book Title
Mathematical Finance
Volume
33
Issue
3
Copyright Statement
© 2023 The Authors. Mathematical Finance published by Wiley Periodicals LLC.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
https://onlinelibrary.wiley.com/doi/full/10.1111/mafi.12390
Publication Status
Published
Date Publish Online
2023-04-11