Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method
AbstractWe 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 InfoPaper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 52_11.
Date of creation: Nov 2011
Date of revision:
optimal execution; market impact; ordinary di?erential equations;
Other versions of this item:
- M. Marzo & D. Ritelli & P. Zagaglia, 2011. "Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method," Working Papers wp797, Dipartimento Scienze Economiche, Universita' di Bologna.
- Massmiliano, Marzo & Daniele, Ritelli & Paolo, Zagaglia, 2011. "Optimal trading execution with nonlinear market impact: an alternative solution method," MPRA Paper 35393, University Library of Munich, Germany.
- Massimiliano Marzo & Daniele Ritelli & Paolo Zagaglia, 2011. "Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method," Papers 1111.6826, arXiv.org.
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-10 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- 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.
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Discussion Papers (IRES - Institut de Recherches Economiques et Sociales)
2004026, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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- BOUCEKKINE, Raouf & RUIZ-TAMARIT, Ramon, 2004. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," CORE Discussion Papers 2004084, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BOUCEKKINE, Raouf & RUIZ-TAMARIT, José Ramon, . "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," CORE Discussion Papers RP -2003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
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