Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest. (Q1413384)

According to the Sparre Andersen model, the surplus at time \(t\) is given by \[ U(t)=u+ct-Z(t),\;t\geq 0 \] where \(c>0\) is the rate of premium income, \(Z(t)\) is the aggregate claim amount up to time \(t\) and \(U(0)=u\). In the paper this model is modified, assuming that the insurer receives interest on the surplus at a constant continuously compound force of interest \(\delta\). So, denoted by \(\tau_{\delta}\) the time of ruin for the modified surplus process, the ultimate ruin probability is given by \[ \psi_{\delta}(u) =Pr\{\tau_{\delta}<\infty\}. \] The authors provide exponential type upper bounds for \(\psi_{\delta}(u)\) by means of martingale and recursive techniques. Moreover numerical comparisons of the upper bounds obtained by each techniques are presented.