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Game-Theoretic Position Building with Market Impact

Article arXiv papers · Author: Neil A. Chriss
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Summary

The paper models traders building stock positions over a fixed period while competing with other traders pursuing the same task. Each trader chooses a trading strategy and seeks a best response to the strategies of their competitors, making the problem a game over strategy choices.

Trading costs reflect both temporary and permanent market impact from the aggregate trading activity of all participants. The paper defines equilibrium strategies, establishes that equilibria exist, and gives closed-form solutions. The supplied description does not state the assumptions behind those results, show the solutions, or report empirical tests, so it provides a high-level account rather than enough detail to assess how the framework performs in live markets.

Key ideas

  • Position building can be framed as a game in which traders respond to competitors’ strategies.
  • Trading costs include temporary and permanent market impact from aggregate activity.
  • The paper establishes the existence of equilibrium strategies and provides closed-form solutions.
  • The available description does not specify model assumptions or empirical validation.

Tags

EquitiesExecutionMarket microstructure
Full text
# Optimal position-building strategies in competition


# Optimal position-building strategies in competition









This paper develops a mathematical framework for building a position in a stock over a fixed period of time while in competition with one or more other traders doing the same thing. We develop a game-theoretic framework that takes place in the space of trading strategies where action sets are trading strategies and traders try to devise best-response strategies to their adversaries. In this setup trading is guided by a desire to minimize the total cost of trading arising from a mixture of temporary and permanent market impact caused by the aggregate level of trading including the trader and the competition. We describe a notion of equilibrium strategies, show that they exist and provide closed-form solutions.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.