Optimal trading: a model predictive control approach

TL;DR

This paper introduces a model predictive control approach to optimize dynamic trading strategies within a linear quadratic regulator framework, incorporating price mean-reversion and constraints for smoother, more effective execution.

Contribution

It develops a novel MPC-based method for optimal trading that ensures positive participation rates and improves upon traditional LQR strategies with a closed-form solution and dark pool integration.

Findings

The proposed method produces smoother trading curves with better completion adherence.

Inclusion of positivity constraints prevents undesirable round-trip trades.

The approach can be simplified to a closed-form solution in continuous trading scenarios.

Abstract

We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including a price mean-reversion signal into the optimization program, in a trading environment where market impact is linear and stage costs are quadratic, we obtain an optimal trading curve that reacts opportunistically to price changes while retaining its ability to satisfy smooth or hard completion constraints. The optimal allocation is affine in the spot price and in the number of outstanding shares at any time, and it can be fully derived iteratively. It is also aggressive in the money, meaning that it accelerates whenever the price is favorable, with an intensity that can be calibrated by the practitioner. Since the LQR may yield locally negative participation rates (i.e round trip trades) which are often undesirable, we show that the aforementioned optimization problem can be improved and solved under positivity constraints following a Model Predictive Control (MPC) approach. In particular, it is smoother and more consistent with the completion constraint than putting a hard floor on the participation rate. We finally examine how the LQR can be simplified in the continuous trading context, which allows us to derive a closed formula for the trading curve under further assumptions, and we document a two-step strategy for the case where trades can also occur in an additional dark pool.