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Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

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  • Kensuke Ishitani
  • Takashi Kato

Abstract

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.

Suggested Citation

  • Kensuke Ishitani & Takashi Kato, 2015. "Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact," Papers 1506.02789, arXiv.org, revised Aug 2015.
    • Handle: RePEc:arx:papers:1506.02789
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    References listed on IDEAS

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    1. Takashi Kato, 2009. "An Optimal Execution Problem with Market Impact," Papers 0907.3282, arXiv.org, revised Dec 2014.
    2. Takashi Kato, 2014. "An optimal execution problem with market impact," Finance and Stochastics, Springer, vol. 18(3), pages 695-732, July.
    3. Naoki Makimoto & Yoshihiko Sugihara, 2010. "Optimal Execution of Multiasset Block Orders under Stochastic Liquidity," IMES Discussion Paper Series 10-E-25, Institute for Monetary and Economic Studies, Bank of Japan.
    4. 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.
    5. 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.
    6. Takashi Kato, 2011. "An Optimal Execution Problem with a Geometric Ornstein-Uhlenbeck Price Process," Papers 1107.1787, arXiv.org, revised Jul 2014.
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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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