Inverting the Transforms Arising in the \(GI/M/1\) Risk Process Using Roots
We consider an insurance risk model for which the claim arrival process is a renewal process and the sizes of claims occur an exponentially distributed random variable. For this risk process, we give an explicit expression for the distribution of probability of ultimate ruin, the expected time to ruin and the distribution of deficit at the time of ruin, using Padé-Laplace method. We have derived results about ultimate ruin probability and the time to ruin in the renewal risk model from its dual queueing model. Also, we derive the bounds for the moments of recovery time. Finally, some numerical results have been presented in the form of tables which compare these results with some of the existing results available in the literature.