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Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets

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  • Alexander Schied
  • Torsten Schöneborn

Abstract

We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann-Morgenstern investor in the liquidity model of Almgren (2003). Using a stochastic control approach, we characterize the value function and the optimal strategy as classical solutions of nonlinear parabolic partial differential equations. We furthermore analyze the sensitivities of the value function and the optimal strategy with respect to the various model parameters. In particular, we find that the optimal strategy is aggressive or passive in-the-money, respectively, if and only if the utility function displays increasing or decreasing risk aversion. Surprisingly, only few further monotonicity relations exist with respect to the other parameters. We point out in particular that the speed by which the remaining asset position is sold can be decreasing in the size of the position but increasing in the liquidity price impact.
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Suggested Citation

  • Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    • Handle: RePEc:spr:finsto:v:13:y:2009:i:2:p:181-204
    DOI: 10.1007/s00780-008-0082-8
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    1. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    2. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
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    4. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
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    10. Schied, Alexander & Schöneborn, Torsten, 2007. "Optimal Portfolio Liquidation for CARA Investors," MPRA Paper 5075, University Library of Munich, Germany.
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    More about this item

    Keywords

    Optimal liquidation; Optimal trade execution; Aggressive in the money; Passive in the money; Liquidity risk; Market impact; Absolute risk aversion; Hamilton–Jacobi–Bellman equation; Nonlinear partial differential equation; Sensitivity analysis; 91B28; 93E20; 60G35; G11; G33;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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