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 Gaussian inter-claim time distributions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
