Optimal Trade Execution Under Endogenous Order Flow

How should a large investor trade when their actions influence—and are influenced by—others in the market? This paper investigates optimal execution in financial markets where order flow is endogenous and governed by self-exciting dynamics. Market order arrivals are modeled using a Hawkes process, with intensity shaped by the trader’s own activity—capturing a feedback loop between execution and market response. The study considers both risk-neutral and risk-averse investors under market impact, deriving closed-form and semi–closed-form optimal strategies. In the risk-averse case, the solution skews execution toward earlier periods to mitigate inventory risk. The model is also extended to more general Hawkes kernels, enhancing practical applicability. The findings shed light on how sophisticated traders can minimize execution costs while accounting for the risk of being tracked in increasingly transparent markets. This work offers actionable insights for algorithmic execution under realistic microstructure dynamics.