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The distribution of tax payments in a Lévy insurance risk model with a surplus-dependent taxation structure. (English) Zbl 1231.91230
Summary: We study the distribution of tax payments in the model of A. Kyprianou and X. Zhou [J. Appl. Probab. 46, No. 4, 1146–1156 (2009; Zbl 1210.60098)], that is a Lévy insurance risk model with a surplus-dependent tax rate. More precisely, after a short discussion on the so-called tax identity, we derive a recursive formula for arbitrary moments of the discounted tax payments until ruin and we identify the distribution of the tax payments when there is no force of interest.

##### MSC:
 91B30 Risk theory, insurance (MSC2010) 60G51 Processes with independent increments; Lévy processes 91B64 Macroeconomic theory (monetary models, models of taxation)
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##### References:
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