A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is pre-specified. The analysis of such control problems is motivated by models of optimal portfolio liquidation.
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- 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.
- Paulwin Graewe & Ulrich Horst & Eric S\'er\'e, 2013.
"Smooth solutions to portfolio liquidation problems under price-sensitive market impact,"
1309.0474, arXiv.org, revised Jun 2017.
- Paulwin Graewe & Ulrich Horst & Eric Séré, 2017. "Smooth Solutions to Portfolio Liquidation Problems under Price-Sensitive Market Impact ," Post-Print hal-01540537, HAL.
- 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. Full references (including those not matched with items on IDEAS)
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