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Asymptotics of Ruin Probabilities in a Subordinated Cramér-Lundberg Model

Author

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  • Klinge, Jonathan

    (Center for Mathematical Economics, Bielefeld University)

  • Schmeck, Maren Diane

    (Center for Mathematical Economics, Bielefeld University)

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 Lévy 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

  • Klinge, Jonathan & Schmeck, Maren Diane, 2026. "Asymptotics of Ruin Probabilities in a Subordinated Cramér-Lundberg Model," Center for Mathematical Economics Working Papers 765, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:765
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    File URL: https://pub.uni-bielefeld.de/download/3014100/3014101
    File Function: First Version, 2026
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