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The probability and severity of ruin for combinations of exponential claim amount distributions and their translations. (English) Zbl 0637.62101
In the classical compound Poisson model of the collective risk theory let \(\psi\) (u,y) denote the probability that ruin occurs and that the negative surplus at the time of ruin is less than -y. It is shown how this function, which also measures the severity of ruin, can be calculated if the claim amount distribution is a translation of a combination of exponential distributions. Furthermore, these results can be applied to a certain discrete time model.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62E15 Exact distribution theory in statistics
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