An insensitivity property of Lundberg's estimate for delayed claims

Abstract

This short note shows that the Lundberg exponential upper bound in the ruin problem of non-life insurance with compound Poisson claims is also valid for the Poisson shot noise delayed-claims model, and that the optimal exponent depends only on the distribution of the total claim per accident, not on the time it takes to honour the claim. This result holds under Cramer's condition.