Abstract
This paper introduces a novel Inventory Pressure Control (IPC) framework for High-Frequency Trading (HFT). Moving beyond traditional stochastic optimal control models, our approach utilizes a specific parametric nonlinear feedback control to define the necessary bid/ask quotes. It incorporates some market indicators such as volatility, order flow imbalance, and toxic order flow. We establish the local stochastic stability of the resulting closed-loop inventory dynamics, proving that the process remains bounded in probability. This local stability framework provides a robust foundation for an integrated profit-risk optimization using the Dynamic Programming (DP) principle. We demonstrate the local profitability of the proposed optimal IPC strategy and validate our theoretical results through an illustrative example.