Climate-Adjusted Ruin under Finite Horizons: Extending the Cramér–Lundberg Model with Covariate-Dependent Claims

Introduction:
Climate change has intensified the frequency and severity of weather-related insurance losses, particularly in portfolios exposed to flood and hydrological risk. Classical ruin models generally assume stationary claim dynamics and therefore do not explicitly account for environmental drivers of risk. This study develops a Climate-Adjusted Ruin framework for non-life insurance in which claim frequency and claim severity are modeled as functions of exogenous climate covariates.

Methods:
We consider a collective risk model and extend the classical Cramér–Lundberg framework by introducing climate-dependent claim frequency and severity components. The aggregate loss process is driven by a covariate-dependent counting distribution for claim arrivals and a conditional severity distribution linked to rainfall and temperature through regression-based specifications. The premium rate is fixed at the technical level calibrated under a baseline scenario, allowing an isolated assessment of the impact of climate deterioration on the insurer’s surplus. Finite-horizon ruin probabilities are evaluated via Monte Carlo simulation under alternative climate stress scenarios. Additionally, we construct risk maps and climate-adjusted capital maps describing, respectively, the sensitivity of ruin probabilities and required initial capital to varying environmental conditions.

Results:
The numerical analysis indicates that adverse climate conditions lead to simultaneous increases in expected claim frequency and loss severity, producing a nonlinear amplification of aggregate losses. This effect weakens surplus accumulation and results in a material increase in ruin probabilities over the planning horizon. The corresponding capital maps show a systematic upward shift in the minimum capital required to satisfy a fixed solvency target under joint precipitation–temperature stress scenarios.

Conclusions:
These findings suggest that solvency assessments based on stationary assumptions may significantly underestimate ruin risk in climate-sensitive portfolios. The proposed framework provides an actuarially interpretable and operational approach for integrating environmental covariates into ruin theory, supporting enhanced stress testing, capital adequacy assessment, and climate-aware risk management.