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

  • Alexander Schied


  • Torsten Schöneborn


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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Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 13 (2009)
Issue (Month): 2 (April)
Pages: 181-204

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Handle: RePEc:spr:finsto:v:13:y:2009:i:2:p:181-204
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  1. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
  2. Umut Cetin & L.C.G. Rogers, 2007. "Modeling liquidity effects in discrete time," LSE Research Online Documents on Economics 2844, London School of Economics and Political Science, LSE Library.
  3. Schoeneborn, Torsten & Schied, Alexander, 2007. "Liquidation in the Face of Adversity: Stealth Vs. Sunshine Trading, Predatory Trading Vs. Liquidity Provision," MPRA Paper 5548, University Library of Munich, Germany.
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  7. Aur\'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756,, revised Feb 2010.
  8. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
  9. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
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  11. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474.
  12. Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October.
  13. Schied, Alexander & Schöneborn, Torsten, 2007. "Optimal Portfolio Liquidation for CARA Investors," MPRA Paper 5075, University Library of Munich, Germany.
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  16. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Science & Finance (CFM) working paper archive 0307332, Science & Finance, Capital Fund Management.
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