IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v13y2009i2p181-204.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-008-0082-8
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
    4. 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.
    5. Schied, Alexander & Schöneborn, Torsten, 2007. "Optimal Portfolio Liquidation for CARA Investors," MPRA Paper 5075, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    9. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    10. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474, October.
    11. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29, January.
    12. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    13. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Torsten Schöneborn, 2016. "Adaptive basket liquidation," Finance and Stochastics, Springer, vol. 20(2), pages 455-493, April.
    2. Kashyap, Ravi, 2020. "David vs Goliath (You against the Markets), A dynamic programming approach to separate the impact and timing of trading costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    4. Schied, Alexander & Schöneborn, Torsten, 2007. "Optimal Portfolio Liquidation for CARA Investors," MPRA Paper 5075, University Library of Munich, Germany.
    5. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    6. Samuel N. Cohen & Lukasz Szpruch, 2011. "A limit order book model for latency arbitrage," Papers 1110.4811, arXiv.org.
    7. 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.
    8. Hai-Chuan Xu & Wei Chen & Xiong Xiong & Wei Zhang & Wei-Xing Zhou & H Eugene Stanley, 2016. "Limit-order book resiliency after effective market orders: Spread, depth and intensity," Papers 1602.00731, arXiv.org, revised Feb 2017.
    9. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    10. Antje Fruth & Torsten Schöneborn & Mikhail Urusov, 2014. "Optimal Trade Execution And Price Manipulation In Order Books With Time-Varying Liquidity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 651-695, October.
    11. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    12. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2006. "Random walks, liquidity molasses and critical response in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 115-123.
    13. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    14. 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.
    15. Dimitri Vayanos & Jiang Wang, 2012. "Market Liquidity -- Theory and Empirical Evidence," NBER Working Papers 18251, National Bureau of Economic Research, Inc.
    16. Seungki Min & Costis Maglaras & Ciamac C. Moallemi, 2018. "Cross-Sectional Variation of Intraday Liquidity, Cross-Impact, and their Effect on Portfolio Execution," Papers 1811.05524, arXiv.org.
    17. Zhao, Jingdong & Zhu, Hongliang & Li, Xindan, 2018. "Optimal execution with price impact under Cumulative Prospect Theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1228-1237.
    18. Saran Ahuja & George Papanicolaou & Weiluo Ren & Tzu-Wei Yang, 2016. "Limit order trading with a mean reverting reference price," Papers 1607.00454, arXiv.org, revised Nov 2016.
    19. Enzo Busseti & Fabrizio Lillo, 2012. "Calibration of optimal execution of financial transactions in the presence of transient market impact," Papers 1206.0682, arXiv.org.
    20. repec:dau:papers:123456789/7391 is not listed on IDEAS
    21. Peter Kratz & Torsten Schoneborn, 2012. "Portfolio liquidation in dark pools in continuous time," Papers 1201.6130, arXiv.org, revised Aug 2012.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:13:y:2009:i:2:p:181-204. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: http://www.springer.com .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.