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Optimal execution with nonlinear impact functions and trading-enhanced risk

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Author Info
Robert F. Almgren
Abstract

Optimal trading strategies are determined for liquidation of a large single-asset portfolio to minimize a combination of volatility risk and market impact costs. The market impact cost per share is taken to be a power law function of the trading rate, with an arbitrary positive exponent. This includes, for example, the square root law that has been proposed based on market microstructure theory. In analogy to the linear model, a 'characteristic time' for optimal trading is defined, which now depends on the initial portfolio size and decreases as execution proceeds. A model is also considered in which uncertainty of the realized price is increased by demanding rapid execution; it is shown that optimal trajectories are described by a 'critical portfolio size' above which this effect is dominant and below which it may be neglected.

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Publisher Info
Article provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 10 (2003)
Issue (Month): 1 (January)
Pages: 1-18
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Handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:1-18

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Related research
Keywords: Market Impact; Trading Strategy; Liquidity Modeling;

Cited by:
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  1. Ryosuke Ishii, 2009. "Optimal Execution in an Evolutionary Setting," KIER Working Papers 670, Kyoto University, Institute of Economic Research. [Downloadable!]
  2. Schoeneborn, Torsten & Schied, Alexander, 2007. "Liquidation in the Face of Adversity: Stealth Vs. Sunshine Trading, Predatory Trading Vs. Liquidity Provision," MPRA Paper 5548, University Library of Munich, Germany. [Downloadable!]
  3. Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  4. Schied, Alexander & Schoeneborn, Torsten, 2008. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," MPRA Paper 7105, University Library of Munich, Germany. [Downloadable!]
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This page was last updated on 2009-12-10.


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