On the computation of upper approximations to ultimate ruin probabilities in case of DFR claimsize distributions

In the present note we consider the classical continuous time model of the collective theory of risk under the assumption that the claimsize distribution is DFR (decreasing failure rate) so that, according to well known queueing results, the ultimate ruin probability turns out to be convex. This property is exploited to develop a stable recursive formula for the calculation of a numerical upper approximation to the ultimate ruin probability with a remarkable improvement over analogous existing algorithms. Numerical results are reported to show the merits of the proposed approach.