Trade Execution Games in a Markovian Environment

Masamitsu Ohnishi and Makoto Shimoshimizu

Applied Mathematical Finance, 2024, vol. 31, issue 4, 239-277

Abstract: This paper examines trade execution games for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor, called Markovian environment, that exogenously affects the market price into financial market modeling. 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.

Date: 2024
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DOI: 10.1080/1350486X.2025.2479498

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