Insurance risk models in a heterogeneous time-dependent population: scaling limits and ruin probabilities

Epidemic dynamics introduce time-varying heterogeneity into insured populations, as individuals' risk profiles depend on their evolving health status, thereby challenging classical insurance models based on homogeneity.

Motivated by this phenomenon, we develop in this paper actuarial risk models in which the claim process is directly linked to an underlying general stochastic population dynamics, resulting in interacting subpopulations with different claim frequencies and severities.

We propose both collective and individual modeling frameworks that track the changing composition of the insured population and its impact on aggregate claims.

For these models, we derive scaling limits and provide bounds and approximations for ruin probabilities, offering tractable tools for risk assessment.

Applications in an SIS context are detailed for different classes of risk processes, thereby contributing to a better understanding of how contagion-driven changes in population structure affect insurer solvency and supporting more realistic modeling of insurance portfolios in the presence of epidemic risk.