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Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies

Author

Listed:
  • Ulrich Horst

    (Humboldt-Universität zu Berlin)

  • Evgueni Kivman

    (Humboldt-Universität zu Berlin)

Abstract

We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio process converges to the solution of an optimal liquidation problem with general semimartingale controls when the instantaneous impact factor converges to zero. Our results provide a unified framework within which to embed the two most commonly used modelling frameworks in the liquidation literature and provide a foundation for the use of semimartingale liquidation strategies and the use of portfolio processes of unbounded variation. Our convergence results are based on novel convergence results for BSDEs with singular terminal conditions and novel representation results of BSDEs in terms of uniformly continuous functions of forward processes.

Suggested Citation

  • Ulrich Horst & Evgueni Kivman, 2024. "Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies," Finance and Stochastics, Springer, vol. 28(3), pages 759-812, July.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:3:d:10.1007_s00780-024-00536-2
    DOI: 10.1007/s00780-024-00536-2
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    References listed on IDEAS

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    7. Ulrich Horst & Xiaonyu Xia, 2019. "Multi-dimensional optimal trade execution under stochastic resilience," Finance and Stochastics, Springer, vol. 23(4), pages 889-923, October.
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    Cited by:

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    More about this item

    Keywords

    Portfolio liquidation; Singular BSDE; Stochastic liquidity; Singular control;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G19 - Financial Economics - - General Financial Markets - - - Other

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