be used to approximate the distribution function of S$_{t}$ , and can be used to estimate probabilities, including tail probabilities. Being finite-sample estimates, these probabilities should have a measure of uncertainty attached. This is obviously an issue for regulation, where the requirement is often to demonstrate that for some s$_{0}$ which reflects the insurer’s available capital, and some κ$_{0}$ spec- ified by the regulator. For Solvency II, κ$_{0}$ = 0 . 005 for one-year total losses. A Monte Carlo point estimate of p$_{0}$ := Pr( S$_{1}$ ≥ s$_{0}$ ) which was less than κ$_{0}$ would be much more reassuring if the whole of the 95% confidence interval for p$_{0}$ were less than κ$_{0}$ , than if the 95% confidence interval contained κ$_{0}$ . A similar problem is faced in ecotoxicology, where one recommendation would be equivalent in this context to requiring that the upper bound of a 95% confidence interval for p$_{0}$ is no greater than κ$_{0}$ ; see Hickey and Hart (2013). If we adopt this approach, though, it is incorrect simply to monitor the upper bound and stop sampling when it drops below κ$_{0}$ , because the confidence interval in this case ought to account for the stochastic stopping rule, rather than being based on a fixed sample size. But it is possible to do a design calculation to suggest an appropriate value for n , the sample size, that will ensure that the upper bound will be larger than κ$_{0}$ with specified probability, a priori , as we now discuss. Let u$_{1}$$_{−}$$_{α}$ ( x ; n ) be the upper limit of a level (1 − α ) confidence interval for p$_{0}$ , where x is the number of sample members that are at least s$_{0}$ , and n 10 Pr( S$_{1}$ ≥ s$_{0}$ ) ≤ κ$_{0}$