Trade execution games in a Markovian environment

TL;DR

This paper models a trade execution game with two large traders in a Markovian environment, deriving explicit strategies and analyzing how environmental uncertainties influence trading behavior.

Contribution

It introduces a Markov game framework for trade execution, incorporating stochastic environmental factors and providing explicit equilibrium strategies.

Findings

Explicit closed-form execution strategies derived

Strategies are generally dynamic and non-randomized

Simulation results align with real market features

Abstract

This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties affect the large traders' execution strategies. We formulate an expected utility maximization problem for two large traders as a Markov game model. Applying the backward induction method of dynamic programming, we provide an explicit closed-form execution strategy at a Markov perfect equilibrium. Our theoretical results reveal that the execution strategy generally lies in a dynamic and non-randomized class; it becomes deterministic if the Markovian environment is also deterministic. In addition, our simulation-based numerical experiments suggest that the execution strategy captures various features observed in financial markets.