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

Ulrich Horst () and Evgueni Kivman ()
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Ulrich Horst: Humboldt-Universität zu Berlin
Evgueni Kivman: Humboldt-Universität zu Berlin

Finance and Stochastics, 2024, vol. 28, issue 3, No 4, 759-812

Abstract: 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.

Keywords: Portfolio liquidation; Singular BSDE; Stochastic liquidity; Singular control; 93E20; 91B70; 60H30 (search for similar items in EconPapers)
JEL-codes: G11 G12 G19 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-024-00536-2

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