Abstract
This article provides a computational formula for the the stability of the probability of ruin of the compound Poisson risk process. This stability is the infinitesimal standardized variation of the probability of ruin resulting from pointwise perturbation of the distribution of the individual claim amounts. The proposed formula is obtained from the saddlepoint approximation to the distribution of the geometric sum, where the distribution of the summands, which is the tail integration of the individual claim amounts distribution, is perturbed by the uniform distribution. A numerical illustration with the compound Poisson risk process with Weibull distributed individual claim amounts is provided.
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