Smooth Solutions to Portfolio Liquidation Problems under Price-Sensitive Market Impact

Paulwin Graewe, Ulrich Horst and Eric Séré ()
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Paulwin Graewe: Department of Mathematics - HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin
Eric Séré: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price-dependent impact functions describing the trading costs in the primary market and price-dependent adverse selection costs associated with dark pool trading. We prove that the value function can be characterized in terms of the unique smooth solution to a PDE with singular terminal value, establish its explicit asymptotic behavior at the terminal time, and give the optimal trading strategy in feedback form.

Keywords: portfolio liquidation; stochastic optimal control; singular terminal value (search for similar items in EconPapers)
Date: 2018-03-01
New Economics Papers: this item is included in nep-mst
Note: View the original document on HAL open archive server: https://hal.science/hal-01540537v1
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Citations: View citations in EconPapers (7)

Published in Stochastic Processes and their Applications, 2018, 128 (3), pp.979-1006. ⟨10.1016/j.spa.2017.06.013⟩

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Working Paper: Smooth solutions to portfolio liquidation problems under price-sensitive market impact (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01540537

DOI: 10.1016/j.spa.2017.06.013

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