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A sample-path approach to optimal position liquidation

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  • Pavlo Krokhmal
  • Stanislav Uryasev

Abstract

We consider the problem of optimal position liquidation where the expected cash flow stream due to transactions is maximized in the presence of temporary or permanent market impact. A stochastic programming approach is used to construct trading strategies that differentiate decisions with respect to the observed market conditions, and can accommodate various types of trading constraints. As a scenario model, we use a collection of sample paths representing possible future realizations of state variable processes (price, trading volume etc.), and employ a heuristical technique of sample-path grouping, which can be viewed as a generalization of the standard nonanticipativity constraints. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Pavlo Krokhmal & Stanislav Uryasev, 2007. "A sample-path approach to optimal position liquidation," Annals of Operations Research, Springer, vol. 152(1), pages 193-225, July.
    • Handle: RePEc:spr:annopr:v:152:y:2007:i:1:p:193-225:10.1007/s10479-006-0143-3
    DOI: 10.1007/s10479-006-0143-3
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    References listed on IDEAS

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    1. Keim, Donald B. & Madhavan, Ananth, 1995. "Anatomy of the trading process Empirical evidence on the behavior of institutional traders," Journal of Financial Economics, Elsevier, vol. 37(3), pages 371-398, March.
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    4. 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.
    5. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    6. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. Dimitris Bertsimas & Shimrit Shtern & Bradley Sturt, 2023. "A Data-Driven Approach to Multistage Stochastic Linear Optimization," Management Science, INFORMS, vol. 69(1), pages 51-74, January.
    2. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
    3. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.
    4. Churlzu Lim & Hanif Sherali & Stan Uryasev, 2010. "Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization," Computational Optimization and Applications, Springer, vol. 46(3), pages 391-415, July.
    5. Julien Vaes & Raphael Hauser, 2018. "Optimal Trade Execution with Uncertain Volume Target," Papers 1810.11454, arXiv.org, revised Sep 2021.

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