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Mathematical Finance
Article . 2023 . Peer-reviewed
License: CC BY
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Article . 2023
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Article . 2021 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2021
License: CC BY
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Trading with the Crowd

Trading with the crowd
Authors: Eyal Neuman; Moritz Voß;

Trading with the Crowd

Abstract

AbstractWe 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 . In addition, we prove that the mean field optimal strategy provides an approximate Nash‐equilibrium for the finite‐player game.

Country
United Kingdom
Keywords

Quantitative Finance - Trading and Market Microstructure, 330, Probability (math.PR), mean field games, Mean field games (aspects of game theory), optimal stochastic control, crowding, predictive signals, Trading and Market Microstructure (q-fin.TR), FOS: Economics and business, 49N80, 49N90, 93E20, 60H30, Stochastic games, stochastic differential games, optimal portfolio liquidation, Portfolio theory, FOS: Mathematics, Optimal stochastic control, price impact, Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
22
Top 10%
Top 10%
Top 10%
Green
hybrid