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

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  • Jonathan Klinge
  • Maren Diane Schmeck

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.

Suggested Citation

  • Jonathan Klinge & Maren Diane Schmeck, 2026. "Asymptotics of Ruin Probabilities in a Subordinated Cram\'er-Lundberg Model," Papers 2603.01821, arXiv.org.
    • Handle: RePEc:arx:papers:2603.01821
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    References listed on IDEAS

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