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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.

##### MSC:
 91B30 Risk theory, insurance (MSC2010) 60K05 Renewal theory 60K10 Applications of renewal theory (reliability, demand theory, etc.)
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##### References:
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