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The compound binomial model with randomized decisions on paying dividends. (English) Zbl 1147.91349
Summary: Consider a discrete time risk process based on the compound binomial model. The insurer pays a dividend of 1 with a probability \(q_{0}\) when the surplus is greater than or equal to a non-negative integer \(x\). We derive recursion formulas and an asymptotic estimate for the ruin probability, the probability function of the surplus prior to the ruin time, and the severity of ruin, etc.

91B30 Risk theory, insurance (MSC2010)
60K05 Renewal theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
Full Text: DOI
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