A Stochastic LQR Model for Child Order Placement in Algorithmic Trading

18 Pages Posted: 7 May 2020

See all articles by Jackie Shen

Jackie Shen

Financial Services, New York

Date Written: March 25, 2020


Modern Algorithmic Trading ("Algo") allows institutional investors and traders to liquidate or establish big security positions in a fully automated or low-touch manner. Most existing academic or industrial Algos focus on how to "slice" a big parent order into smaller child orders over a given time horizon. Few models rigorously tackle the actual placement of these child orders. Instead, placement is mostly done with a combination of empirical signals and heuristic decision processes. A self-contained, realistic, and fully functional Child Order Placement (COP) model may never exist due to all the inherent complexities, e.g., fragmentation due to multiple venues, dynamics of limit order books, lit vs. dark liquidity, different trading sessions and rules. In this paper, we propose a reductionism COP model that focuses exclusively on the interplay between placing passive limit orders and sniping using aggressive takeout orders. The dynamic programming model assumes the form of a stochastic linear-quadratic regulator (LQR) and allows closed-form solutions under the backward Bellman equations. Explored in detail are model assumptions and general settings, the choice of state and control variables and the cost functions, and the derivation of the closed-form solutions.

Keywords: child order placement, dynamic programming, LQR, delay cost, spread cost, impact cost, Poisson hits, passive, aggressive, Bellman equation, optimal policy, positive matrix

JEL Classification: C02, C44, C61, G14, G24

Suggested Citation

Shen, Jackie, A Stochastic LQR Model for Child Order Placement in Algorithmic Trading (March 25, 2020). Available at SSRN: https://ssrn.com/abstract=3574365 or http://dx.doi.org/10.2139/ssrn.3574365

Jackie Shen (Contact Author)

Financial Services, New York ( email )

United States

HOME PAGE: http://alum.mit.edu/www/jhshen

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics