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Exponential behavior in the presence of dependence in risk theory. (English) Zbl 1097.62110
Summary: We consider an insurance portfolio situation in which there is possible dependence between the waiting time for a claim and its actual size. By employing the underlying random walk structure we obtain explicit exponential estimates for infinite- and finite-time ruin probabilities in the case of light-tailed claim sizes. The results are illustrated in several examples, worked out for specific dependence structures.

62P05 Applications of statistics to actuarial sciences and financial mathematics
60G50 Sums of independent random variables; random walks
91B30 Risk theory, insurance (MSC2010)
60K05 Renewal theory
Full Text: DOI Euclid
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