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Optimal Basket Liquidation for CARA Investors is Deterministic

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  • Alexander Schied
  • Torsten Schoneborn
  • Michael Tehranchi
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    Abstract

    We consider the problem faced by an investor who must liquidate a given basket of assets over a finite time horizon. The investor's goal is to maximize the expected utility of the sales revenues over a class of adaptive strategies. We assume that the investor's utility has constant absolute risk aversion (CARA) and that the asset prices are given by a very general continuous-time, multiasset price impact model. Our main result is that (perhaps surprisingly) the investor does no worse if he narrows his search to deterministic strategies. In the case where the asset prices are given by an extension of the nonlinear price impact model of Almgren [(2003) Applied Mathematical Finance, 10, pp. 1-18], we characterize the unique optimal strategy via the solution of a Hamilton equation and the value function via a nonlinear partial differential equation with singular initial condition.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 17 (2010)
    Issue (Month): 6 ()
    Pages: 471-489

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    Handle: RePEc:taf:apmtfi:v:17:y:2010:i:6:p:471-489

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    Related research

    Keywords: Market impact modelling; illiquid markets; optimal liquidation; optimal trade execution; algorithmic trading; utility maximization; Hamilton-Jacobi-Bellman equation; finite fuel control;

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    Cited by:
    1. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Papers 1204.0148, arXiv.org, revised Jun 2013.
    2. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org.
    3. Aur\'elien Alfonsi & Alexander Schied & Florian Kl\"ock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised May 2014.
    4. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    5. Mauricio Junca, 2011. "Stochastic impulse control on optimal execution with price impact and transaction cost," Papers 1103.3482, arXiv.org, revised Jan 2013.
    6. Olivier Gu\'eant, 2012. "Execution and block trade pricing with optimal constant rate of participation," Papers 1210.7608, arXiv.org, revised Dec 2013.
    7. Olivier Gu\'eant, 2013. "Permanent market impact can be nonlinear," Papers 1305.0413, arXiv.org, revised Mar 2014.
    8. Olivier Gu\'eant & Jiang Pu & Guillaume Royer, 2013. "Accelerated Share Repurchase: pricing and execution strategy," Papers 1312.5617, arXiv.org, revised Jan 2014.
    9. 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.
    10. Olivier Gu\'eant, 2012. "Optimal execution and block trade pricing: a general framework," Papers 1210.6372, arXiv.org, revised Jul 2014.
    11. Alexander Schied & Tao Zhang, 2013. "A state-constrained differential game arising in optimal portfolio liquidation," Papers 1312.7360, arXiv.org, revised May 2014.
    12. Olivier Gu\'eant & Guillaume Royer, 2013. "VWAP execution and guaranteed VWAP," Papers 1306.2832, arXiv.org, revised May 2014.
    13. Olivier Gu\'eant & Jiang Pu, 2013. "Option pricing and hedging with execution costs and market impact," Papers 1311.4342, arXiv.org, revised Aug 2014.

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