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On the distribution of the surplus prior to and at ruin. (English) Zbl 1129.62425
Summary: Consider a classical compound Poisson model. The safety loading can be positive, negative or zero. Explicit expressions for the distributions of the surplus prior and at ruin are given in terms of the ruin probability. Moreover, the asymptotic behaviour of these distributions as the initial capital tends to infinity are obtained. In particular, for positive safety loading the Cramér case, the case of subexponential distributions and some intermediate cases are discussed.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
62E20 Asymptotic distribution theory in statistics
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