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Parisian ruin for a refracted Lévy process. (English) Zbl 1394.60046
Summary: In this paper, we investigate Parisian ruin for a Lévy surplus process with an adaptive premium rate, namely a refracted Lévy process. Our main contribution is a generalization of the result in [R. Loeffen et al., Bernoulli 19, No. 2, 599–609 (2013; Zbl 1267.60054)] for the probability of Parisian ruin of a standard Lévy insurance risk process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also considered. Despite the more general setup considered here, our main result is as compact and has a similar structure. Examples are provided.

60G51 Processes with independent increments; Lévy processes
91B30 Risk theory, insurance (MSC2010)
Full Text: DOI
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