Asymptotics of Ruin Probabilities in a Subordinated Cramér-Lundberg Model

Jonathan Klinge and Maren Diane Schmeck
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Jonathan Klinge: Center for Mathematical Economics, Bielefeld University
Maren Diane Schmeck: Center for Mathematical Economics, Bielefeld University

No 765, Center for Mathematical Economics Working Papers from 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.

Keywords: Cramér-Lundberg Model; Ruin-Theory; Subordination; Subexponential Distribution; Regular Variation (search for similar items in EconPapers)
Pages: 31
Date: 2026-02-20
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:765

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