Table VI: Timings for the methods shown in Figure 6. non-random case with θ = 0 (Table IV), with the exception of the Panjer method, which takes longer because it scales linearly with the upper limit on the horizontal axis. Now consider the case where the single-event loss is capped at $5 m. The implementation of this cap is straightforward, and we describe it in the Appendix. The results are given in Figure 6 and Table VI. For the timings, the main effect of the cap is on the Panjer method, because the cap reduces the probability in the righthand tail of the loss distribution, and allows us to use a smaller upper limit on the horizontal axis. But the Panjer approximation, where it can be computed, still takes a thousand times longer to compute than the Moment bound. Finally, consider expanding the time period from t = 1 to t = 10 years; the results are given in Figure 7 and Table VII. The timings of the Markov, 6.5 Ten-year losses 6.4 Capping the loss from a single event 25 d = − 4 d = − 3 d = − 2 d = − 1 d = 0 Panjer 0.275 11.950 NA NA NA MonteCarlo 1.106 2.099 5.625 10.329 11.837 Moment 0.016 0.070 0.210 0.355 0.431 Chernoff 0.508 2.057 5.659 10.853 14.992 Cantelli 0.003 0.006 0.019 0.032 0.041