Smooth solutions to portfolio liquidation problems under price-sensitive market impact

Paulwin Graewe, Ulrich Horst and Eric S\'er\'e

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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.

Date: 2013-09, Revised 2017-06
New Economics Papers: this item is included in nep-mst
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Working Paper: Smooth Solutions to Portfolio Liquidation Problems under Price-Sensitive Market Impact (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1309.0474

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