Revisiting Trade-sign Long-memory and Square-root Law price impact

Battle Count: 79

Highly relevant for quantitative trading, particularly for algorithmic execution and market impact modeling. The paper provides a unified theoretical foundation for two critical empirical regularities (square-root impact and LMF long-memory) that directly inform execution algorithm design, order splitting strategies, and participation rate calibration. The explicit separation of event time, operational time, and calendar time is practically important for understanding how execution timing affects realized impact. However, the paper is purely theoretical without empirical validation or implementation guidance, limiting its direct applicability.

Extremely high mathematical complexity. The paper involves coupled PDEs, free-boundary problems, Green function methods, Volterra integral equations, renewal theory, discrete time random walks, and subordination theory. Implementing the discrete reaction-diffusion model would require careful handling of non-uniform event times, front tracking, and source terms. The continuum limit and Volterra equation derivation require advanced mathematical physics techniques. No code or numerical procedures are provided.

The paper provides complete mathematical derivations with numbered equations (Eq. 1-69), making the theoretical framework fully reproducible analytically. However, there is no accompanying code, no empirical data, and no numerical simulations provided. The derivations are self-contained but require significant mathematical expertise to verify. No GitHub repository or supplementary materials are mentioned.