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Optimal Order Scheduling for Deterministic Liquidity Patterns

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  • Peter Bank
  • Antje Fruth
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    Abstract

    We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. By contrast to the previous literature, see, e.g., Obizhaeva and Wang (2005), Predoiu, Shaikhet, and Shreve (2011), we allow the liquidity parameters of market depth and resilience to vary deterministically over the course of the trading period. The resulting singular optimal control problem is shown to be tractable by methods from convex analysis and, under minimal assumptions, we construct an explicit solution to the scheduling problem in terms of some concave envelope of the resilience adjusted market depth.

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    File URL: http://arxiv.org/pdf/1310.3077
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    Paper provided by arXiv.org in its series Papers with number 1310.3077.

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    Date of creation: Oct 2013
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    Handle: RePEc:arx:papers:1310.3077

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    1. Aurélien Alfonsi & José Infante Acevedo, 2012. "Optimal execution and price manipulations in time-varying limit order books," Working Papers hal-00687193, HAL.
    2. Tarun Chordia, 2001. "Market Liquidity and Trading Activity," Journal of Finance, American Finance Association, vol. 56(2), pages 501-530, 04.
    3. Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
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