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Finite time ruin probabilities with one Laplace inversion. (English) Zbl 1074.91026

Summary: We present an explicit formula for the Laplace transform in time of the finite time ruin probabilities of a classical Levy model with phase-type claims. Our result generalizes the ultimate ruin probability formula of S. Asmussen and T. Rolski [ibid. 10, 259–274 (1991; Zbl 0748.62058)] – see also the analog queuing formula for the stationary waiting time of the M/Ph/1 queue in M. F. Neuts [Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD, (1981; Zbl 0469.60002)] – and it considers the deficit at ruin as well.

MSC:

91B30 Risk theory, insurance (MSC2010)
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