A Generalized Langevin Model of Latent Liquidity and Concave Price Impact

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Highly relevant for institutional traders and quants dealing with large orders. It provides a mechanistic derivation of the square-root impact law and offers insights into how liquidity depletion and memory affect execution costs and post-trade price recovery.

Implementing the GLE with a Markovian lift requires handling systems of stochastic differential equations with memory kernels. The exact lift simplifies simulation compared to non-Markovian methods, but parameter estimation and calibration remain complex.

The paper provides detailed baseline parameters (Table 1), numerical methods (drift-implicit midpoint scheme), and verification procedures (Monte Carlo and PINN comparisons). However, calibration to real market data is deferred to a companion paper, limiting immediate empirical reproducibility.