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

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Author Info
Schied, Alexander
Schoeneborn, Torsten

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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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7105.

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Date of creation: 08 Feb 2008
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Handle: RePEc:pra:mprapa:7105

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Related research
Keywords: Liquidity illiquid markets optimal liquidation strategies dynamic trading strategies algorithmic trading utility maximization

Other versions of this item:

Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
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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  1. 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. [Downloadable!] (restricted)
  2. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Blackwell Publishing, vol. 11(4), pages 447-474. [Downloadable!] (restricted)
  3. Schied, Alexander & Schöneborn, Torsten, 2007. "Optimal Portfolio Liquidation for CARA Investors," MPRA Paper 5075, University Library of Munich, Germany. [Downloadable!]
  4. 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. [Downloadable!]
  5. He, Hua & Mamaysky, Harry, 2005. "Dynamic trading policies with price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 891-930, May. [Downloadable!] (restricted)
  6. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March. [Downloadable!] (restricted)
  7. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November. [Downloadable!] (restricted)
  8. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April. [Downloadable!] (restricted)
  9. Robert F. Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor and Francis Journals, vol. 10(1), pages 1-18, January. [Downloadable!] (restricted)
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This page was last updated on 2008-11-18.


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