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

TL;DR

This paper develops a continuous-time stochastic control model for optimal execution of market and limit orders, incorporating trade speed limits, fill uncertainty, and penalty terms to improve trading strategies.

Contribution

It introduces a novel model combining trade speed control and fill uncertainty, providing explicit strategies and conditions for optimality in order execution.

Findings

Optimal strategies depend on model parameters and impact costs.

Numerical simulations illustrate the effectiveness of the proposed controls.

Conditions for finiteness and optimality are derived.

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.