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Discounted probabilities and ruin theory in the compound binomial model. (English) Zbl 1013.91063
A discrete-time model is considered. The aggregate claims are modeled as a compound binomial process. The possible claim amounts are integral multiples of the annual premium. The main goal of the paper is to study the function $$f(x,y;u)$$, which is the “discounted” probability of ruin, given an initial surplus of $$u$$, such that the surplus just before ruin is $$x$$, and the deficit $$dt$$ ruin is $$y$$. Applications include an explicit expression for the expected discounted value of a payment 1 at the time of ruin and formulas for the expected time of ruin.

##### MSC:
 91B30 Risk theory, insurance (MSC2010)
##### Keywords:
risk theory; ruin probability; compound binomial model
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##### References:
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