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On the ruin time distribution for a Sparre Andersen process with exponential claim sizes. (English) Zbl 1141.91486
Summary: We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of D. C. M. Dickson et al. [Scand. Actuar. J. 2005, No. 5, 358–376 (2005; Zbl 1144.91025)] for such processes with Erlang inter-claim times. The derivation is based on transforming the original boundary crossing problem to an equivalent one on linear lower boundary crossing by a spectrally positive Lévy process. We illustrate our result in the cases of gamma, mixed exponential and inverse Gaussian inter-claim time distributions.

MSC:
91B30 Risk theory, insurance (MSC2010)
60G40 Stopping times; optimal stopping problems; gambling theory
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