Optimal position-building strategies in competition

TL;DR

This paper introduces a game-theoretic model for optimal position-building in stock trading, accounting for competition and market impact, and provides explicit equilibrium strategies.

Contribution

It develops a novel mathematical framework for competitive trading strategies with explicit equilibrium solutions and existence proofs.

Findings

Existence of equilibrium strategies in competitive trading

Closed-form solutions for optimal strategies

Insights into market impact effects on trading behavior

Abstract

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.