Beyond the Copula: A Survey of Artificial Intelligence Methods for Modeling Reserve Dependence in Non-Life Insurance

Hajar Ettaya, Tarek Zari

Traditional copulas, although they have revolutionized dependence modeling by separating marginal structures from joint structures, present fundamental limitations when faced with complex, asymmetric, or highdimensional dependencies. This paper examines to what extent machine learning models and neural copulas can overcome these limitations. Through a synthetic analysis of recent developments — including IGNIS parametric estimation networks, GARCH-RBM models, deep neural copulas, and copula-nested spectral kernel networks — we demonstrate that neural approaches offer unprecedented flexibility for capturing structures that classical copulas cannot reproduce. However, this expressive superiority comes with challenges in terms of interpretability, numerical stability, and theoretical guarantees. We conclude that hybridization between statistical rigor and the representative power of neural networks constitutes the most promising path for modeling complex dependencies.