On the ruin time distribution for a Sparre Andersen process with exponential claim sizes

By Konstantin Borovkov, D. Dickson. 2007

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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 Dickson et al. [Dickson, D.C.M., Hughes, B.D., Zhang, L., 2005. The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims. Scand. Actuar. J., 358-376] 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 Levy process. We illustrate our result in the cases of gamma, mixed exponential and inverse Gaussian inter-claim time distributions.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a7eb8cfb64f4cf665c4ee0ad8f0eaeda996f8fda