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Discrete-Time Optimal Execution Under A Generalized Price Impact Model With Markovian Exogenous Orders

Author

Listed:
  • MASAAKI FUKASAWA

    (Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan2Center for Mathematical Modeling and Data Science, Osaka University, Osaka 560-8531, Japan)

  • MASAMITSU OHNISHI

    (Center for Mathematical Modeling and Data Science, Osaka University, Osaka 560-8531, Japan3Graduate School of Economics, Osaka University, Osaka 560-0043, Japan)

  • MAKOTO SHIMOSHIMIZU

    (Graduate School of Management, Tokyo Metropolitan University, Tokyo 100-0005, Japan)

Abstract

This paper examines a discrete-time optimal execution problem with generalized price impact. Our main objective is to investigate the effect of price impact caused by aggregate random trade orders posed by small traders on the optimal execution strategy when orders of the small traders have a Markovian dependence. Our problem is formulated as a Markov decision process with state variables which include the last small traders’ aggregate orders. Over a finite horizon, a large trader with Constant Absolute Risk Aversion (CARA) von Neumann–Morgenstern (vN-M) utility function maximizes the expected utility from the final wealth. By applying the backward induction method of dynamic programming, we characterize the optimal execution strategy and optimal value function and conclude that the optimal execution strategy is a time-dependent affine function of three state variables. Moreover, numerical analysis prevails that the optimal execution strategy admits a “statistical arbitrage” via a round-trip trading, although our model considers a linear permanent price impact. The result differs from the previous prevailing one that a linear permanent price impact model precludes any price manipulation or arbitrage. Thus, considering a price impact caused by small traders’ orders with a Markovian dependence is significant.

Suggested Citation

  • Masaaki Fukasawa & Masamitsu Ohnishi & Makoto Shimoshimizu, 2021. "Discrete-Time Optimal Execution Under A Generalized Price Impact Model With Markovian Exogenous Orders," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-43, August.
    • Handle: RePEc:wsi:ijtafx:v:24:y:2021:i:05:n:s0219024921500254
    DOI: 10.1142/S0219024921500254
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    Citations

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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.

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