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Classification of the Bounds on the Probability of Ruin for Lévy Processes with Light-tailed Jumps

Abstract : In this note, we study the ultimate ruin probabilities of a real-valued Lévy process X with light-tailed negative jumps. It is well-known that, for such Lévy processes, the probability of ruin decreases as an exponential function with a rate given by the root of the Laplace exponent, when the initial value goes to infinity. Under the additional assumption that X has integrable positive jumps, we show how a finer analysis of the Laplace exponent gives in fact a complete description of the bounds on the probability of ruin for this class of Lévy processes. This leads to the identification of a case that is not considered in the literature and for which we give an example. We then apply the result to various risk models and in particular the Cramér-Lundberg model perturbed by Brownian motion.
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https://hal.archives-ouvertes.fr/hal-01597828
Contributor : Jerome Spielmann Connect in order to contact the contributor
Submitted on : Thursday, February 22, 2018 - 5:34:06 PM
Last modification on : Wednesday, November 3, 2021 - 6:05:21 AM
Long-term archiving on: : Wednesday, May 23, 2018 - 3:00:42 PM

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  • HAL Id : hal-01597828, version 2
  • ARXIV : 1709.10295

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Jérôme Spielmann. Classification of the Bounds on the Probability of Ruin for Lévy Processes with Light-tailed Jumps. 2018. ⟨hal-01597828v2⟩

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