Computing ruin probability in the classical risk model

We consider the classical risk model with discrete time and loss distribution with heavy tails. When computing the ruin probability, a region of medium values of the argument, which is most interesting in practice, arises. In this region, known asymptotic formulas do not work yet, while direct solutions of the corresponding linear integral equations do not work already. We construct sufficiently accurate and efficient algorithms for computing the ruin probability in this region, which are based on approximating the loss distribution with a family of exponential distributions. To test the results, we have conducted a numerical experiment.