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

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

2007-09-06

arxiv.org/abs/0709.0764v1

Mathematics

Probability

12 pages, 2 figures

Scientific paper

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. (2005) for such
processes with Erlang inter-claim times. We illustrate our result in the cases
of gamma and mixed exponential inter-claim time distributions.

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