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A note on joint occupation times of spectrally negative Lévy risk processes with tax. (English) Zbl 1392.60044

Summary: In this paper we consider the joint Laplace transform of occupation times over disjoint intervals for spectrally negative Lévy processes with a general loss-carry-forward taxation structure. This tax structure was first introduced by H. Albrecher and C. Hipp in their paper [Bl. DGVFM 28, No. 1, 13–28 (2007; Zbl 1119.62103)]. We obtain representations of the joint Laplace transforms in terms of scale functions and the Lévy measure associated with the driven spectrally negative Lévy processes. Two numerical examples, i.e. a Brownian motion with drift and a compound Poisson model, are provided at the end of this paper and explicit results are presented with discussions.

MSC:

60G51 Processes with independent increments; Lévy processes
60E10 Characteristic functions; other transforms

Citations:

Zbl 1119.62103
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References:

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