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Web of Proceedings - Francis Academic Press
Web of Proceedings - Francis Academic Press

Mathematical Modeling of the Stability of the Insurance Market in the Coastal Area of Florida

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DOI: 10.25236/iwmecs.2025.041

Author(s)

Yuxuan Ouyang

Corresponding Author

Yuxuan Ouyang

Abstract

This study develops a unified simulation framework to analyze the stability and equity of coastal property‐insurance markets under non stationary climate risk. We couple a climate adjusted hazard generator—modeled as a non homogeneous compound Poisson process with heavy tailed severities—with agent based representations of heterogeneous insurers and income stratified households. Loss formation integrates exposure, fragility, and geographic modifiers; industry pricing embeds risk loads and capital costs with memory of past shocks; household purchase and insurer underwriting decisions co evolve with perceived risk. We evaluate six policy regimes—including reinsurance subsidies, low income premium caps, and structural adaptation—across three hazard trajectories via 100×30 year Monte Carlo simulations. Results demonstrate pronounced nonlinearities: under a high stress climate scenario, systemic insolvency undergoes a phase transition between years 10–20, with failure rates reaching 60–70% absent intervention. Policy bundles that combine structural adaptation and reinsurance support substantially attenuate fragility and price inflation, preserving coverage and containing public exposure. The most comprehensive package sustains average penetration above 80%, reduces insolvency rates to roughly 0.21, and halves expected public outlays by year 30. The framework provides a tractable basis for stress testing, distributional assessment, and policy design in insurance systems exposed to deep climatic uncertainty.

Keywords

Climate risk; Insurance market stability; Agent‑based modeling; Reinsurance policy