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Ruin estimates for large claims. (English) Zbl 0666.62098
The classical Cramér estimate for the probability of ruin in the Cramér-Lundberg model assumes that the claimsizes are exponentially bounded. In the case of large claims (Pareto, log-normal,...) the condition of sub-exponentiality on the integrated claimsize distribution is the relevant one. In this paper, we study a family of distribution functions which is rich enough to contain the most important claimsize models and for which an easily verifiable sufficient condition for sub- exponentiality holds.

62P05 Applications of statistics to actuarial sciences and financial mathematics
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