how much rounding can be performed on a given ELT without materially changing the distribution of t -year total losses. Ideally, this would be as- sessed using an exact calculation, like Panjer recursion. Unfortunately it is precisely because Panjer recursion is so numerically intensive that rounding and merging of large ELTs is necessary in the first place. So instead we assess the effect of rounding and merging using the Moment bound, which, as already established, converges to the actual value when the number of events in the time-interval is large. Figure 2 shows the result of eight different values for d , from − 7 to 0. The outcome with d = − 7 is materially different, which is not surprising because this ELT only has two rows. More intriguing is that the outcome with d = − 6 is almost the same as that with no compression at all, despite the ELT having only 20 rows. Here we consider one-year losses, and treat the losses for each event as cer- tain; i.e. the first case in section 5. The methods we consider are Panjer, Monte Carlo, Moment, Chernoff, Cantelli, and Markov. The first two pro- vide approximately exact values for Pr( S$_{1}$ ≥ s ). Panjer is an approximation because of the need to compress the ELT. For the Monte Carlo method, we used 10 5 simulations, as discussed in section 4, and we report the 95% confidence interval in the tail. The remaining methods provide strict upper bounds on Pr( S$_{1}$ ≥ s ). Our optimisation approach for the Moment and Chernoff bounds is given in the Appendix. All the timings are CPU times in seconds on a MacBook Pro processor 2.53 GHz Intel Core 2 Duo. 6.2 Computational expense of the different methods 18