1 INTRODUCTION One of the objectives in catastrophe modelling is to assess the probability distribution of losses for a specified period, such as a year. From the point of view of an insurance company, the whole of the loss distribution is in- teresting, and valuable in determining insurance premiums. But the shape of the righthand tail is critical, because it impinges on the solvency of the company. A simple measure of the risk of insolvency is the probability that the annual loss will exceed the company’s current operating capital. Im- posing an upper limit on this probability is one of the objectives of the EU Solvency II directive. If a probabilistic model is supplied for the loss process, then this tail probability can be computed, either directly, or by simulation. Shevchenko (2010) provides a survey of the various approaches. This can be a lengthy calculation for complex losses. Given the inevitably subjective nature of quantifying loss distributions, computational resources might be better used in a sensitivity analysis. This requires either a quick approximation to the tail probability or an upper bound on the probability, ideally a tight one. In this paper we present and analyse several different bounds, all of which can be computed quickly from a very general event loss table. By making no assumptions about the shape of the righthand tail beyond the existence of the second moment, our approach extends to fat-tailed distributions. We provide a numerical illustration, and discuss the conditions under which the bound is tight. 2