Asymptotics of Ruin Probabilities in a Subordinated Cram\'er-Lundberg Model
Risk Management
2026-03-03 v1 Probability
Abstract
We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events, this process is time-changed by a L\'evy subordinator. The subordinator is chosen so that it evolves, on average, at the same speed as calendar time, creating a trade-off between intensity and severity. We show that such a transformation always has a negative impact on the probability of ruin. Despite the expected total claim amount remaining invariant, it turns out that the probability of ruin as a function of the initial capital falls arbitrarily slowly depending on the choice of the subordinator.
Keywords
Cite
@article{arxiv.2603.01821,
title = {Asymptotics of Ruin Probabilities in a Subordinated Cram\'er-Lundberg Model},
author = {Jonathan Klinge and Maren Diane Schmeck},
journal= {arXiv preprint arXiv:2603.01821},
year = {2026}
}