Beyond Closed-Form Liquidity Models: An AI-Enhanced Quantitative Approach

Liquidity spreads are a fundamental manifestation of trading frictions in financial markets, with important implications for asset pricing, risk management, and market stability. Classical theoretical models of liquidity typically rely on restrictive assumptions and closed-form specifications that limit their ability to capture nonlinear and adaptive liquidity dynamics observed in modern markets. This paper proposes a novel mathematical framework for liquidity spread estimation that integrates artificial intelligence within a rigorously defined analytical structure. Liquidity spreads are modeled as nonlinear functionals of observable market states, represented by operator-based mappings embedded in suitable function spaces. Artificial intelligence enters the framework through flexible parameterizations of these operators, allowing for endogenous learning of complex liquidity dynamics while preserving theoretical properties such as well-posedness, stability, and interpretability. The model is analyzed using tools from functional analysis and approximation theory, and sufficient conditions for existence, continuity, and robustness are established. By reconciling analytical finance theory with AI-inspired functional representations, the proposed framework extends classical liquidity models and provides a theoretically grounded foundation for future research on liquidity, pricing, and risk in high-dimensional financial markets.