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Optimal Portfolio Liquidation for CARA Investors

  • Schied, Alexander
  • Schöneborn, Torsten

We consider the finite-time optimal portfolio liquidation problem for a von Neumann-Morgenstern investor with constant absolute risk aversion (CARA). As underlying market impact model, we use the continuous-time liquidity model of Almgren and Chriss (2000). We show that the expected utility of sales revenues, taken over a large class of adapted strategies, is maximized by a deterministic strategy, which is explicitly given in terms of an analytic formula. The proof relies on the observation that the corresponding value function solves a degenerate Hamilton-Jacobi-Bellman equation with singular initial condition.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5075.

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Date of creation: 27 Sep 2007
Date of revision:
Handle: RePEc:pra:mprapa:5075
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  1. 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.
  2. Markus K. Brunnermeier & Lasse Heje Pedersen, 2005. "Predatory Trading," Journal of Finance, American Finance Association, vol. 60(4), pages 1825-1863, 08.
  3. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
  4. 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.
  5. 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.
  6. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
  7. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar.
  8. 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.
  9. 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.
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