Figure 1: The effect of sample size on Monte Carlo accuracy. The graph shows the probability that the upper bound of the 95% Jeffreys confidence interval for p$_{0}$ lies below κ$_{0}$ = 0 . 005 when p$_{0}$ = κ$_{0}$/ 2. and computationally cheap upper bound may be of more practical use than an approximation. Section 6.1 also discusses indirect ways to assess the compression error, using the upper bounds. Monte Carlo simulation is an attractive alternative to Panjer recursion, because it comes with a simple assessment of accuracy, is easily parallelis- able, and the sample drawn can be used to calculated other quantities of interest for insurers like the net aggregate loss and reinsurance recovery costs. In this section we consider three tractable special cases. 5 TRACTABLE SPECIAL CASES 12 Size of Monte Carlo sample, n (log scale) Probability of u 0.95 X n 0 1000 2000 5000 10000 0.0 0.2 0.4 0.6 0.8 1.0