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Upper bounds for ultimate ruin probabilities in the Sparre Andersen risk model with interest and a nonlinear dividend barrier. (English) Zbl 1166.60029

The authors derive the Lundberg-type upper bounds for the ultimate ruin probability in the classical risk model with constant force of interest and a nonlinear dividend barrier. More precise upper bounds for the ultimate ruin probabilities are given in case when the claim sizes are exponentially distributed with parameter \(\alpha> 0\).

MSC:

60G51 Processes with independent increments; Lévy processes
62P05 Applications of statistics to actuarial sciences and financial mathematics
65C05 Monte Carlo methods
91B30 Risk theory, insurance (MSC2010)
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