Exactly solvable model for the diffusive price-dynamics paradox under long-range correlated market-order flow

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The paper provides fundamental theoretical insights into price formation mechanisms that are highly relevant to quantitative trading. Understanding the square-root price-impact law and its role in maintaining diffusive price dynamics is crucial for: (1) optimal execution algorithms that minimize market impact, (2) understanding why price dynamics appear Brownian despite predictable order flow, (3) modeling institutional investor behavior and order splitting, (4) risk management for large positions. However, the paper is primarily theoretical and does not directly propose trading strategies or provide backtested results. Its value is in the foundational understanding it provides for market microstructure modeling.

The core model (discrete-time LMF with square-root impact) is relatively straightforward to implement as a stochastic simulation with M order-splitting traders. The Lévy-walk mapping and exact PDF calculations require advanced knowledge of integral transforms (Fourier, Laplace, z-transforms) and renewal theory. The generalized models (I and II) add complexity with resting states and impact decay. Numerical verification requires careful handling of power-law distributions and long-time asymptotics. The analytical proofs are mathematically sophisticated but the simulation implementation is moderate.

The paper provides complete analytical derivations in appendices and numerical verification through simulations. However, no code repository is explicitly mentioned. The model parameters (δ, α, M, τ_r, τ_D) are clearly specified, and the mathematical framework is fully self-contained. Reproduction would require implementing the discrete/continuous-time stochastic simulations described in the paper.