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Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact


  • Kensuke Ishitani
  • Takashi Kato


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,, revised Jun 2015.
  • Handle: RePEc:arx:papers:1301.6485

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    References listed on IDEAS

    1. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474.
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    Cited by:

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

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