This paper introduces a novel market-making model designed for high-frequency trading in limit order books (LOBs), addressing key shortcomings of the classical Avellaneda-Stoikov framework. The authors define a 'weakly consistent' LOB model that enforces direction and timing consistency: price movements must align with order types (e.g., prices cannot rise on sell market orders). The model classifies orders into twelve types based on aggressiveness and uses marked point processes to capture the discrete, jump-driven nature of prices. The market maker's control problem is formulated as an optimal switching and impulse control problem, leading to a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI) solved numerically via finite differences.

A key contribution is demonstrating that inconsistent LOB models, which allow price movements independent of order flow, can severely overstate market-making profits. In simulated backtests calibrated to ETF data, the authors show profit overstatement exceeding 50%. The model also respects price-time priority and discrete price ticks, making it more applicable to real electronic exchanges. Numerical results illustrate optimal bid-ask spreads as functions of inventory and risk aversion, providing practical insights for high-frequency market makers. The paper bridges the gap between theoretical market-making models and realistic LOB dynamics, offering a more reliable framework for strategy evaluation.