Optimal Execution of Limit and Market Orders with Trade Director, Speed Limiter, and Fill Uncertainty

International Journal of Financial Engineering, Vol. 4, issue 2, p.1750020, 2017

28 Pages Posted: 5 Apr 2016 Last revised: 28 Feb 2019

See all articles by Brian Bulthuis

Brian Bulthuis

KCG Holdings Inc.

Julio Concha

KCG Holdings Inc.

Tim Leung

University of Washington - Department of Applied Math

Brian Ward

Columbia University

Date Written: April 12, 2017

Abstract

We study the optimal execution of market and limit orders with permanent and temporary price impacts as well as uncertainty in the filling of limit orders. Our continuous-time model incorporates a trade speed limiter and a trader director to provide better control on the trading rates. We formulate a stochastic control problem to determine the optimal dynamic strategy for trade execution, with a quadratic terminal penalty to ensure complete liquidation. In addition, we identify conditions on the model parameters to ensure optimality of the controls and finiteness of the associated value functions. For comparison, we also solve the schedule-following optimal execution problem that penalizes deviations from an order schedule. Numerical results are provided to illustrate the optimal market and limit orders over time.

Suggested Citation

Bulthuis, Brian and Concha, Julio and Leung, Tim and Ward, Brian, Optimal Execution of Limit and Market Orders with Trade Director, Speed Limiter, and Fill Uncertainty (April 12, 2017). International Journal of Financial Engineering, Vol. 4, issue 2, p.1750020, 2017 , Available at SSRN: https://ssrn.com/abstract=2758418 or http://dx.doi.org/10.2139/ssrn.2758418

Brian Bulthuis

KCG Holdings Inc. ( email )

545 Washington Boulevard
Jersey City, NJ 07310
United States

Julio Concha

KCG Holdings Inc. ( email )

545 Washington Boulevard
Jersey City, NJ 07310
United States

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Brian Ward

Columbia University ( email )

New York, NY
United States

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