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C\`adl\`ag semimartingale strategies for optimal trade execution in stochastic order book models

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  • Julia Ackermann
  • Thomas Kruse
  • Mikhail Urusov

Abstract

We analyze 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 for trading in both directions and for c\`adl\`ag semimartingales as execution strategies. We derive a quadratic BSDE that under appropriate assumptions characterizes minimal execution costs and 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 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, 2020. "C\`adl\`ag semimartingale strategies for optimal trade execution in stochastic order book models," Papers 2006.05863, arXiv.org, revised Jul 2021.
    • Handle: RePEc:arx:papers:2006.05863
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    References listed on IDEAS

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    4. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2020. "Optimal trade execution in an order book model with stochastic liquidity parameters," Papers 2006.05843, arXiv.org, revised Apr 2021.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Ulrich Horst & Evgueni Kivman, 2021. "Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies," Papers 2103.05957, arXiv.org, revised Jul 2023.
    4. 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.
    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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