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Ruin probabilities in classical risk models with gamma claims. (English) Zbl 1416.91166

Summary: In this paper, we provide three equivalent expressions for ruin probabilities in a Cramér-Lundberg model with gamma distributed claims. The results are solutions of integro-differential equations, derived by means of (inverse) Laplace transforms. All the three formulas have infinite series forms, two involving Mittag-Leffler functions and the third one involving moments of the claims distribution. This last result applies to any other claim size distributions that exhibits finite moments.

MSC:

91B30 Risk theory, insurance (MSC2010)
44A10 Laplace transform
33E12 Mittag-Leffler functions and generalizations
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