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A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions

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  • Paulwin Graewe
  • Ulrich Horst
  • Jinniao Qiu

Abstract

We establish existence and uniqueness results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of a non-Markovian stochastic control optimal problem in which the terminal state of the controlled process is prespecified. The analysis of such control problems is motivated by models of optimal portfolio liquidation.

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File URL: http://arxiv.org/pdf/1309.0461
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Paper provided by arXiv.org in its series Papers with number 1309.0461.

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Date of creation: Sep 2013
Date of revision: Mar 2014
Handle: RePEc:arx:papers:1309.0461

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Web page: http://arxiv.org/

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  1. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
  2. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
  3. Paulwin Graewe & Ulrich Horst & Eric S\'er\'e, 2013. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Papers 1309.0474, arXiv.org, revised Dec 2013.
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