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Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact

  • Kensuke Ishitani
  • Takashi Kato
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    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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    Paper provided by in its series Papers with number 1301.6485.

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    Date of creation: Jan 2013
    Date of revision: Jun 2015
    Publication status: Published in Communications on Stochastic Analysis 9(1), 113-129 (2015)
    Handle: RePEc:arx:papers:1301.6485
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    1. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474.
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