Explicit Signal-Adaptive Sequential Optimal Execution Quotes

Battle Count: 86

This paper is directly and highly relevant to quantitative trading. It provides a complete, explicit solution framework for optimal execution through sequential limit-order placement, which is a core problem in algorithmic trading. The signal-adaptive nature of the quotes makes it directly applicable to modern execution systems that incorporate predictive signals from order-flow imbalance, LOB dynamics, or ML-based forecasts. The four execution criteria cover the full spectrum from risk-neutral to risk-averse execution. The explicit formulas enable real-time implementation without numerical PDE solving.

The explicit formulas are closed-form and computationally efficient, requiring only evaluation of finite sums (divided-difference formulas) for the triangular system. The main complexity lies in: (1) correctly implementing the triangular recursion for w(t,q) across inventory levels, (2) handling the degenerate vs. non-degenerate cases for coefficients A_q, (3) implementing the frozen-signal adaptive update for time-varying signals, and (4) projecting onto admissible quote bounds. The mathematical structure is elegant but requires careful numerical handling of potential near-degenerate cases (A_i close to A_j).

The paper provides fully explicit closed-form formulas for all four cases, making the theoretical results highly reproducible. Parameter values for numerical experiments are specified in Table 1. However, no code repository or supplementary computational scripts are mentioned. The frozen-coefficient implementation for time-dependent signals is described but not provided as code. The mathematical derivations are complete with proofs in appendices.