A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for testing this problem and consider both parametric and non-parametric estimators of the individual claim amount distribution. Simulation studies show that the suggested boot-strap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

Keywords: Edgeworth expansion, exponential and log-normal claim amounts, normal approximation, P-value, pivotal quantity, resampling, second-order accuracy.