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A Lévy insurance risk process with tax. (English) Zbl 1144.60032
Summary: Using fluctuation theory, we solve the two-sided exit problem and identify the ruin probability for a general spectrally negative Lévy risk process with tax payments of a loss-carry-forward type. We study arbitrary moments of the discounted total amount of tax payments and determine the surplus level to start taxation which maximises the expected discounted aggregate income for the tax authority in this model. The results considerably generalise those for the Cramér-Lundberg risk model with tax.

##### MSC:
 60G51 Processes with independent increments; Lévy processes 91B30 Risk theory, insurance (MSC2010) 60J75 Jump processes (MSC2010)
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