Optimal Trading with Speed-Dependent Transaction Cost Rates: A Flexible Framework.

This article focuses on developing a flexible continuous-time model for optimal trade execution that incorporates speed-dependent transaction cost rates (TCRs), which often exhibit irregular shapes in real-world limit order books. The model approximates general TCR functions using piecewise linear forms and characterizes optimal trading strategies that balance risk exposure and transaction costs, producing empirically observed patterns such as order-shredding and U-shaped trading speeds over time for large trades. Applying the framework to small-cap stocks, the authors demonstrate that common naive strategies—instant liquidation, constant speed trading, or assuming linear TCRs—can lead to significant utility losses. The study further shows that the model-based strategy outperforms simpler benchmarks out-of-sample and extends to both liquidation and acquisition problems, highlighting the importance of accounting for speed-dependent transaction costs in optimal portfolio execution.