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Optimal Asset Liquidation with Multiplicative Transient Price Impact

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  • Dirk Becherer
  • Todor Bilarev
  • Peter Frentrup

Abstract

We study a multiplicative transient price impact model for an illiquid financial market, where trading causes price impact which is multiplicative in relation to the current price, transient over time with finite rate of resilience, and non-linear in the order size. We construct explicit solutions for the optimal control and the value function of singular optimal control problems to maximize expected discounted proceeds from liquidating a given asset position. A free boundary problem, describing the optimal control, is solved for two variants of the problem where admissible controls are monotone or of bounded variation.

Suggested Citation

  • Dirk Becherer & Todor Bilarev & Peter Frentrup, 2015. "Optimal Asset Liquidation with Multiplicative Transient Price Impact," Papers 1501.01892, arXiv.org, revised Apr 2017.
    • Handle: RePEc:arx:papers:1501.01892
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    References listed on IDEAS

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    Cited by:

    1. Torben Koch & Tiziano Vargiolu, 2019. "Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem," Papers 1911.04223, arXiv.org.
    2. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2016. "Optimal Liquidation under Stochastic Liquidity," Papers 1603.06498, arXiv.org, revised Nov 2017.
    3. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Mar 2018.
    4. Almendra Awerkin & Tiziano Vargiolu, 2021. "Optimal installation of renewable electricity sources: the case of Italy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1179-1209, December.
    5. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2018. "Optimal liquidation under stochastic liquidity," Finance and Stochastics, Springer, vol. 22(1), pages 39-68, January.
    6. Dirk Becherer & Todor Bilarev, 2018. "Hedging with physical or cash settlement under transient multiplicative price impact," Papers 1807.05917, arXiv.org, revised Jun 2023.

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