Journal article

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

Konstantin A Borovkov, David CM Dickson

INSURANCE MATHEMATICS & ECONOMICS | ELSEVIER SCIENCE BV | Published : 2008

Abstract

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 Lévy process. We illustrate our result in the cases of gamma, mixed exponential and inverse Gaus..

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