2023 Australasian Actuarial Education and Research Symposium

Eric Cheung

UNSW Sydney

Cumulative Parisian ruin in finite and infinite time horizons in a renewal risk process

This is joint work with Wei Zhu

In this presentation, we consider the cumulative Parisian ruin problem in a renewal risk model with general interclaim times and exponential claims, where the cumulative Parisian ruin time is the first time the total time spent by the surplus process below level zero exceeds a certain time length. The infinite-time cumulative Parisian ruin probabilities are derived under a deterministic Parisian clock and under an Erlang clock, where the latter case can also serve as an approximation of the former. The finite-time cumulative Parisian ruin probability is subsequently analyzed when the time horizon is another Erlang random variable. Our formulas can be easily applied in numerical examples where the interclaim times follow gamma, Weibull, or Pareto distributions. We demonstrate that the choice of the interclaim distribution does have a significant impact on the cumulative Parisian ruin probabilities when one deviates from the exponential assumption.