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Optimal and equilibrium execution strategies with generalized price impact

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  • Masamitsu Ohnishi
  • Makoto Shimoshimizu

Abstract

This paper examines the execution problems of large traders with a generalized price impact. Constructing two related models in a discrete-time setting, we solve these problems by applying the backward induction method of dynamic programming. In the first problem, we formulate the expected utility maximization problem of a single large trader as a Markov decision process and derive an optimal execution strategy. Then, in the second model, we formulate the expected utility maximization problem of two large traders as a Markov game and derive an equilibrium execution strategy at a Markov perfect equilibrium. Both of these two models enable us to investigate how the execution strategies and trade performances of a large trader are affected by the existence of other traders. Moreover, we find that these optimal and equilibrium execution strategies become deterministic when the total execution volumes of non-large traders are deterministic. We also show, by some numerical examples, the comparative statics results with respect to several problem parameters.

Suggested Citation

  • Masamitsu Ohnishi & Makoto Shimoshimizu, 2020. "Optimal and equilibrium execution strategies with generalized price impact," Quantitative Finance, Taylor & Francis Journals, vol. 20(10), pages 1625-1644, October.
    • Handle: RePEc:taf:quantf:v:20:y:2020:i:10:p:1625-1644
    DOI: 10.1080/14697688.2020.1749294
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    Cited by:

    1. Héctor Jasso-Fuentes & Carlos G. Pacheco & Gladys D. Salgado-Suárez, 2023. "A discrete-time optimal execution problem with market prices subject to random environments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 562-583, October.
    2. Masamitsu Ohnishi & Makoto Shimoshimizu, 2024. "Trade execution games in a Markovian environment," Papers 2405.07184, arXiv.org.
    3. Masamitsu Ohnishi & Makoto Shimoshimizu, 2022. "Optimal Pair–Trade Execution with Generalized Cross–Impact," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 253-289, June.

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