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A First Step Toward a CAT Model Framework
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Resumo(s)
This paper presents a physics-based hazard model for catastrophe (CAT) modelling of urban flood risk—a first step toward a complete CAT modelling framework. We introduce a linear second-order ordinary differential equation (ODE) system to simulate the underlying mechanisms of water accumulation, absorption, routing, and drainage across interconnected surfaces in densely built urban areas. The model treats an urban zone as a multivariate network of surfaces, each with unique hydrological properties, linked by directed water flows. For risk analysis, the external meteorological forcing (representing the precipitation input) is randomised. Our risk-analysis protocol relies on a Monte Carlo simulation of stochastic forcing. Its reliability is founded on rigorous mathematical properties proven for the ODE system (existence, uniqueness, positivity, monotonicity, and a priori bounds), ensuring that the probabilistic outputs are well-defined and physically plausible. A three-surface example illustrates the framework and a complete risk analysis is performed, yielding concrete risk metrics that inform mitigation strategies. Computational efficiency is shown to be optimal for linear ODE systems, outperforming generic methods. This work provides a foundational, physics-informed hazard model for next-generation CAT models, directly supporting the insurance industry’s adaptation to climate change.
Descrição
Publisher Copyright: © 2026 by the authors.
Palavras-chave
Catastrophe model Flood modelling Hazard module of a CAT model Linear ordinary differential equations modelling Risk analysis Accounting Economics, Econometrics and Finance (miscellaneous) Strategy and Management SDG 13 - Climate Action