On the density and moments of the time of ruin with exponential claims. (English) Zbl 1062.60007

Summary: The probability density function of the time of ruin in the classical model with exponential claim sizes is obtained directly by inversion of the associated Laplace transform. This result is then used to obtain explicit closed-form expressions for the moments. The form of the density is examined for various parameter choices.


60E05 Probability distributions: general theory
60E10 Characteristic functions; other transforms
91B30 Risk theory, insurance (MSC2010)
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