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

Jérôme Spielmann
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Jérôme Spielmann: LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Bounds; Laplace exponent; Lévy processes; MSC 2010 subject classifications: 91B30; 60G51; Ruin probabilities; Perturbed model; Lundberg equation; Laplace exponent; Lévy processes; Lundberg equation; Per- turbed model; Ruin probabilities (search for similar items in EconPapers)
Date: 2018-02-22
New Economics Papers: this item is included in nep-rmg
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