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<p>The dramatic growth in institutionally managed assets, coupled with the advent of Internet trading and electronic brokerage for retail investors, has led to a surge in the size and volume of trading. At the same time, competition in the asset-management industry has increased to where fractions of a percent in performance can separate the top funds from those in the next tier. In this environment, portfolio managers have begun to explore active management of trading to boost returns. Controlling execution cost can be viewed as a stochastic dynamic optimization problem because trading takes time, stock prices exhibit random fluctuations, and execution prices depend on trade size, order flow, and market conditions. </p> <p>In this article, the authors apply stochastic dynamic programming to derive trading strategies that minimize the expected cost of executing a portfolio of securities over a fixed time period. That is, they derive the optimal sequence of trades as a function of prices, quantities, and other market conditions. To illustrate the practical relevance of these methods, the authors apply them to a hypothetical portfolio of 25 stocks. They estimate the methods' price-impact functions using 1996 trade data and derive the optimal execution strategies. The authors also perform several Monte Carlo simulations to compare the optimal strategy's performance to that of several alternatives. </p>

P. Hummel, A. W. Lo and D. Bertsimas, "Optimal Control of Execution Costs for Portfolios," in Computing in Science & Engineering, vol. 1, no. , pp. 40-53, 1999.
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