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Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact

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  • Kensuke Ishitani
  • Takashi Kato

Abstract

We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise part. Then, we derive a continuous-time model as a limit of a discrete-time value function. We find that the continuous-time value function is characterized by a stochastic control problem with a Levy process.

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  • Kensuke Ishitani & Takashi Kato, 2013. "Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact," Papers 1301.6485, arXiv.org, revised Jun 2015.
    • Handle: RePEc:arx:papers:1301.6485
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    4. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474, October.
    5. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
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    Cited by:

    1. Takashi Kato, 2017. "An Optimal Execution Problem with S-shaped Market Impact Functions," Papers 1706.09224, arXiv.org, revised Oct 2017.

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