Table IV: Timings for the methods shown in Figure 3, in seconds on a stan- dard desktop computer, for different degrees of rounding (see section 6.1). Figure 3 shows the exceedance probabilities for the methods, computed on 101 equally-spaced ordinates between $0 m and $40 m, with compression d = − 4. The Markov bound is the least effective, and the Cantelli bound is surprisingly good. As expected, the Chernoff and Moment bounds converge, and also, in this case, converge on the Panjer and Monte Carlo estimates. The timings for the methods are given in Table IV. These values require very little elaboration. The Moment, Cantelli, and Markov bounds are ef- fectively instantaneous to compute, with timings of a few thousandths of a second. The Chernoff bound is more expensive but still takes only a frac- tion of a second. The Monte Carlo and Panjer approximations are hundreds, thousands, or even millions of times more expensive. The Panjer bound is impractical to compute at compression below d = − 2 (and from now on we will just consider d ≤ − 3). A similar table to Table IV could be constructed for any specified value s$_{0}$ , rather than a whole set of values. The timings for the Moment, Chernoff, Cantelli, and Markov bounds would all be roughly one hundredth as large, 20 d = − 4 d = − 3 d = − 2 d = − 1 d = 0 Panjer 0.461 40.784 4651.298 NA NA MonteCarlo 1.246 2.085 5.820 10.228 12.413 Moment 0.011 0.006 0.010 0.019 0.025 Chernoff 0.112 0.310 0.634 1.017 1.284 Cantelli 0.001 0.002 0.001 0.002 0.002 Markov 0.001 0.001 0.001 0.005 0.001