Asymptotics of Ruin Probabilities in a Subordinated Cram\'er-Lundberg Model

Jonathan Klinge and Maren Diane Schmeck

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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.

Date: 2026-03
New Economics Papers: this item is included in nep-rmg
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