Mean-field equilibrium of heterogeneous agents under market impact

Battle Count: 80

The paper provides deep theoretical insights into how heterogeneous forecast horizons and market impact interact to determine price regularity and predictability. The rough-signal cancellation condition and the link between Hawkes endogeneity (branching ratio) and forecast endogeneity (α) are directly relevant to understanding why prices appear locally Brownian despite underlying predictability. The results on horizon distribution (Gamma shape parameter ξ) determining whether prices achieve Brownian regularity have implications for understanding the role of high-frequency vs. medium-frequency traders. However, the paper is purely theoretical with no direct trading strategy or implementation guidance.

The paper is entirely theoretical with no code or numerical implementation. The mathematical framework involves Volterra integral equations, Banach space fixed-point theory, Abel resolvents, Neumann series, confluent hypergeometric functions, and Hölder regularity analysis. Implementing the equilibrium kernel computation would require solving the linear fixed-point equation (Id - αD_νI)φ_α = D_νK numerically, handling Gamma-distributed horizon averaging, and computing Volterra convolutions. The theoretical depth and abstract functional-analytic setting make direct implementation very challenging.

The paper is purely theoretical with complete mathematical proofs provided in appendices. All assumptions, propositions, and theorems are rigorously stated and proved. However, there is no code, numerical implementation, or empirical validation. Reproducibility depends on the reader's ability to verify the mathematical arguments. The framework is self-contained with explicit conditions for existence, uniqueness, and regularity results.