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On the time spent in the red by a refracted Lévy risk process. (English) Zbl 1321.60099

In this paper, the author introduces “an insurance ruin model with an adaptive premium rate, henceforth referred to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regular level when the wealth process recovers.” The surplus process under consideration is a Markov semimartingale, or, more concrete a homogeneous diffusion with jumps. “The analysis is focused mainly on the time a refracted Lévy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from [A. E. Kyprianou and R. L. Loeffen, Ann. Inst. Henri Poincaré, Probab. Stat. 46, No. 1, 24–44 (2010; Zbl 1201.60042)] and [R. L. Loeffen et al., Stochastic Processes Appl. 124, No. 3, 1408–1435 (2014; Zbl 1287.60062)],” the author identifies “the distribution of various functionals related to occupation times of refracted spectrally negative Lévy processes. For example, these results are used to compute both the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring” (quotations are taken from the author’s abstract).

MSC:

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

References:

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