Cantelli, Moment, and Chernoff bounds are unaffected by the value of t . The timing for the Panjer method grows with t , because the righthand tail of S$_{t}$ grows with t . The timing for the Monte Carlo method grows roughly linearly with t , but the ‘in simulation’ time for Monte Carlo is dominated by other factors, so the additional computing time for the increase in t from t = 1 to t = 10, is small. We have presented four upper bounds and two approximations for the upper tail of the loss distribution that follows from an Event Loss Table (ELT). We argue that in many situations an upper bound on this probability is sufficient. For example, to satisfy the regulator, in a sensitivity analysis, or when there is supporting evidence that the bound is quite tight. Of the bounds we have considered, we find that the Moment bound offers the best blend of tightness and computational efficiency. In fact, the Moment bound is effectively costless to compute, based on the timings from our R package. We have stressed that there are no exact methods for computing tail Table VII: Timings for the methods shown in Figure 7. 7 SUMMARY 27 d = − 4 d = − 3 d = − 2 d = − 1 d = 0 Panjer 0.587 46.000 NA NA NA MonteCarlo 918.101 2.312 7.189 11.834 14.869 Moment 0.027 0.141 0.435 0.592 0.736 Chernoff 3.989 2.101 7.794 10.503 18.314 Cantelli 0.002 0.007 0.020 0.164 0.046