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Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method

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  • Massimiliano Marzo

    ()
    (Department of Economics, Università di Bologna)

  • Daniele Ritelli

    ()
    (Department of Mathematics, Università di Bologna)

  • Paolo Zagaglia

    ()
    (Department of Economics, Università di Bologna)

Abstract

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time are trade at the beginning of the period. We propose a general solution method that accomodates the case of a positive stock of assets in the initial period. Our ?ndings are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive asset holdings in the initial period, the optimal execution time depends on trading activity at the beginning of the planning period.

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Bibliographic Info

Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 52_11.

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Date of creation: Nov 2011
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Handle: RePEc:rim:rimwps:52_11

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Keywords: optimal execution; market impact; ordinary di?erential equations;

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  1. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
  2. Kraus, Alan & Stoll, Hans R, 1972. "Price Impacts of Block Trading on the New York Stock Exchange," Journal of Finance, American Finance Association, vol. 27(3), pages 569-88, June.
  3. Huang, Roger D & Stoll, Hans R, 1997. "The Components of the Bid-Ask Spread: A General Approach," Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 995-1034.
  4. Jones, Charles M. & Lipson, Marc L., 1999. "Execution Costs of Institutional Equity Orders," Journal of Financial Intermediation, Elsevier, vol. 8(3), pages 123-140, July.
  5. repec:cor:louvrp:2003 is not listed on IDEAS
  6. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
  7. Jones, C.M. & Lipson, M.L., 1999. "Execution Costs of Institutional Equity Orders," Papers 99-1, Columbia - Graduate School of Business.
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