Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets
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.
|Date of creation:||08 Feb 2008|
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- 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.
- Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003.
"Fluctuations and response in financial markets: the subtle nature of `random' price changes,"
cond-mat/0307332, arXiv.org, revised Aug 2003.
- 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.
- Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
- Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
- 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.
- P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
- Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474.
- 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.
- Hua He & Harry Mamaysky, 2001. "Dynamic Trading Policies With Price Impact," Yale School of Management Working Papers ysm244, Yale School of Management, revised 01 Jan 2002.
- Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29.
- 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.
- Schied, Alexander & Schöneborn, Torsten, 2007. "Optimal Portfolio Liquidation for CARA Investors," MPRA Paper 5075, University Library of Munich, Germany.
- Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
- Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
- Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
- Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
- 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.
- Marc Potters & Jean-Philippe Bouchaud, 2002. "More statistical properties of order books and price impact," Science & Finance (CFM) working paper archive 0210710, Science & Finance, Capital Fund Management.
- 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. Full references (including those not matched with items on IDEAS)
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