Optimal control of execution costs
Dimitris Bertsimas, Andrew W Lo *

Abstract
We derive dynamic optimal trading strategies that minimize the expected cost of trading a large block of equity over a fixed time horizon. Specifically, given a fixed block of shares to be executed within a fixed finite number of periods T, and given a price-impact function that yields the execution price of an individual trade as a function of the shares traded and market conditions, we obtain the optimal sequence of trades as a function of market conditions – closed-form expressions in some cases – that minimizes the expected cost of executing within T periods. Our analysis is extended to the portfolio case in which price impact across stocks can have an important effect on the total cost of trading a portfolio.

*Corresponding Author

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