  We examine optimal execution models that take into account both market
microstructure impact and informational costs. Informational footprint is
related to order flow and is represented by the trader's influence on the flow
imbalance process, while microstructure influence is captured by instantaneous
price impact. We propose a continuous-time stochastic control problem that
balances between these two costs. Incorporating order flow imbalance leads to
the consideration of the current market state and specifically whether one's
orders lean with or against the prevailing order flow, key components often
ignored by execution models in the literature. In particular, to react to
changing order flow, we endogenize the trading horizon $T$. After developing
the general indefinite-horizon formulation, we investigate several tractable
approximations that sequentially optimize over price impact and over $T$. These
approximations, especially a dynamic version based on receding horizon control,
are shown to be very accurate and connect to the prevailing Almgren-Chriss
framework. We also discuss features of empirical order flow and links between
our model and "Optimal Execution Horizon" by Easley et al (Mathematical
Finance, 2013).
