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Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models

Author

Listed:
  • Julia Ackermann

    (University of Gießen)

  • Thomas Kruse

    (University of Gießen)

  • Mikhail Urusov

    (University of Duisburg-Essen)

Abstract

We analyse an optimal trade execution problem in a financial market with stochastic liquidity. To this end, we set up a limit order book model in continuous time. Both order book depth and resilience are allowed to evolve randomly in time. We allow trading in both directions and for càdlàg semimartingales as execution strategies. We derive a quadratic BSDE that under appropriate assumptions characterises minimal execution costs, and we identify conditions under which an optimal execution strategy exists. We also investigate qualitative aspects of optimal strategies such as e.g. appearance of strategies with infinite variation or existence of block trades, and we discuss connections with the discrete-time formulation of the problem. Our findings are illustrated in several examples.

Suggested Citation

  • Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models," Finance and Stochastics, Springer, vol. 25(4), pages 757-810, October.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:4:d:10.1007_s00780-021-00464-5
    DOI: 10.1007/s00780-021-00464-5
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Self-exciting price impact via negative resilience in stochastic order books," Papers 2112.03789, arXiv.org, revised Jul 2022.
    2. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2022. "Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems," Papers 2206.03772, arXiv.org, revised Sep 2023.
    3. Alexandre Roch, 2023. "Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    4. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies," Papers 2207.00446, arXiv.org, revised Sep 2023.
    5. Xinman Cheng & Guanxing Fu & Xiaonyu Xia, 2024. "Long Time Behavior of Optimal Liquidation Problems," Papers 2405.14177, arXiv.org.
    6. Tao Chen & Mike Ludkovski & Moritz Vo{ss}, 2022. "On Parametric Optimal Execution and Machine Learning Surrogates," Papers 2204.08581, arXiv.org, revised Oct 2023.

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    More about this item

    Keywords

    Optimal trade execution; Continuous-time stochastic optimal control; Limit order book; Stochastic order book depth; Stochastic resilience; Quadratic BSDE; Infinite-variation execution strategy; Semimartingale execution strategy;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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