Moments of the ruin time in a perturbed Cramér-Lundberg model

We present formulae for the moments of the ruin time in a Lévy risk model. From these we derive the asymptotic behaviour of the moments of the ruin time, as the initial capital tends to infinity. In the perturbed Cramér-Lundberg model with phase-type distributed claims, we explicitely compute the first two moments of the ruin time in terms of roots and derivatives of the corresponding Laplace exponent. In the special case of exponential claims we provide explicit formulae for the first two moments of the ruin time in terms of the model parameters. All our considerations distinguish between the profitable and the unprofitable setting. 2020 Mathematics subject classification. 60G51, 60G40, 91G05

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