# Optimal Control of Execution Costs

## Dimitris Bertsimas

Massachusetts Institute of Technology (MIT) - Sloan School of Management

## Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Sloan School of Management; Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL); National Bureau of Economic Research (NBER)

Undated

LFE-1025-96

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 $\overline{S}$ 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 or "best execution strategy" as a function of market conditions---closed-form expressions in some cases---that minimizes the expected cost of executing $\overline{S}$ 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. We also discuss generalizations to other price impact functions, imposing constraints, and algorithms for performing the optimization numerically. (The text "$\overline{S}$" comes from a text-processor called TeX and stands for a mathematical symbol which is an upper case S with a bar over it.)

JEL Classification: G23

working papers series

#### Suggested Citation

Bertsimas, Dimitris and Lo, Andrew W., Optimal Control of Execution Costs (Undated). LFE-1025-96. Available at SSRN: http://ssrn.com/abstract=7395

#### Contact Information

##### Dimitris Bertsimas
Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )
E53-359
Cambridge, MA 02142
United States
617-253-4223 (Phone)
617-258-7579 (Fax)
##### Andrew W. Lo (Contact Author)
Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )
100 Main Street
E62-618
Cambridge, MA 02142
United States
617-253-0920 (Phone)
781 891-9783 (Fax)
Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)
Stata Center
Cambridge, MA 02142
United States
National Bureau of Economic Research (NBER)
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
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