Philip S. Griffin
Abstract: Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a Levy insurance risk process under the Cramer-Lundberg and convolution equivalent conditions. For example the limiting distributions of the overshoot and the undershoot are strikingly similar in these two settings. This is somewhat surprising since the global sample path behavior of the process under these two conditions is quite different. Using tools from excursion theory and fluctuation theory we provide a unified approach, which explains this connection and leads to new asymptotic results, by describing the evolution of the sample paths from the time of last maximum prior to ruin until ruin occurs.
ArXiv: 1309.6973