probabilities when taking into account limited computing resources. Of the approximately exact methods we consider, we prefer Monte Carlo simulation over Panjer recursion, because of the availability of an error estimate in the former and the amount of information provided by the latter. A back-of-the- envelope calculation suggests that 10,000 Monte Carlo simulations should suffice to satisfy the Solvency II regulator. 

The merging operation is a very useful way to condense an ELT that has become bloated, for example after using mixtures of Gamma distri- butions to represent more complicated secondary uncertainty distributions. We have shown that the Moment bound provides a quick way to assess how much merging can be done without having a major impact on the resulting aggregate loss distribution. 

We have also demonstrated the versatility of the Gamma distribution for single event losses. The Gamma distribution has a simple moment generat- ing function and explicit expressions for the moments. Therefore it fits very smoothly into the compound Poisson process that is represented in an ELT, for the purposes of computing approximations and bounds. We also show how the Gamma distribution can easily be adapted to account for a cap on single event losses. We favour the capped Gamma distribution over the Beta distribution, which is often used in the industry, because the former has an atom (as is appropriate) while the latter does not. 

