This paper proposes a continuous-time optimal execution model that incorporates both market microstructure costs (instantaneous price impact) and informational costs arising from order flow imbalance. The key innovation is the introduction of a stochastic order flow imbalance process, which is influenced by the trader's own actions and captures the informational footprint of trading. The trader minimizes a cost functional that includes quadratic price impact, quadratic informational costs (penalizing trading in unbalanced markets), and inventory risk. The execution horizon is endogenized, allowing the trader to dynamically adjust the speed of liquidation based on current market conditions.

The authors first formulate the problem as a stochastic control problem with an indefinite horizon, leading to a nonlinear HJB equation. To achieve tractability, they propose a two-stage approximation: first fixing the horizon and solving the resulting linear-quadratic problem, then optimizing over the horizon statically. This yields closed-form myopic strategies for popular inventory risk specifications (linear, quadratic, and constant). A receding horizon control approach is then used to dynamically update the optimal horizon as the state variables evolve. Numerical experiments show that this approximation is very accurate compared to the full dynamic solution.

The paper also discusses empirical features of order flow, such as mean reversion and predictability, and provides guidance on calibrating the model parameters. The results highlight the importance of considering order flow imbalance in execution algorithms, as it leads to adaptive strategies that can significantly reduce costs compared to traditional deterministic schedules. The work bridges the gap between microstructure models and informational cost models, offering a practical framework for optimal execution in modern electronic markets.