2017
DOI: 10.1016/j.insmatheco.2017.03.005
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Parisian ruin for a refracted Lévy process

Abstract: Abstract. 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 [13] 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. Example… Show more

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Cited by 21 publications
(27 citation statements)
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“…[1]. For a refracted Lévy process and with a fixed delay for the Parisian ruin time, Lkabous et al [13] determined the Laplace transform of the Parisian ruin time τ r possibly killed when the process goes above a given level.…”
Section: Introductionmentioning
confidence: 99%
“…[1]. For a refracted Lévy process and with a fixed delay for the Parisian ruin time, Lkabous et al [13] determined the Laplace transform of the Parisian ruin time τ r possibly killed when the process goes above a given level.…”
Section: Introductionmentioning
confidence: 99%
“…To deal with the limit as b → ∞, we apply the same machinery using identity (31). We can also compute the limit directly using (10) and (11) and the fact that Then,…”
Section: 1mentioning
confidence: 99%
“…We present a probabilistic analysis and simple resulting expressions for the two-sided exit problem, Laplace transform and the probability of Parisian ruin under a hybrid observation scheme in terms of the delayed scale functions introduced by Lkabous and Renaud [13]. Our approach is based on the expression of the Gerber-Shiu distribution at Parisian ruin with exponential implementation delays obtained in [2], combined with some results in [11].…”
Section: Introductionmentioning
confidence: 99%
“…The authors of [21] revisited the Parisian ruin probability and provided an expression which is considerably simpler than that of [9], and unifies the results for spectrally negative Lévy processes of bounded and of unbounded variation. In [20], the result of [21] was further extended to refracted Lévy processes. The Parisian-ruin-related dividend optimization problem was investigated in [10], where the barrier dividend strategy turned out to be the optimal strategy.…”
Section: Introductionmentioning
confidence: 99%