The moments for the Gamma distribution were given in (5). Starting from this expression and k = 1, we step out in k until the Gamma approximation to log E( S k t ) /s k shows an increase on its previous value. The ceiling of the resulting k is taken as the maximum k value. If the Moment bound is required for a sequence of s values, we use the largest s value in the sequence. Minimisation for the Chernoff bound. The MGF for a Gamma dis- tribution is given in (4). Hence the range for the control variable v is 0 < v < min$_{i}$ { β$_{i}$ } . As explained in section 6.3, we specify the two pa- rameters of the Gamma distribution for event i in terms of the fixed loss x$_{i}$ , now treated as the expected loss, and a coefficient of variation θ (which could vary with i ). This gives β$_{i}$ = 1 / ( θ $^{2}$x$_{i}$ ), and hence In the simpler case of a fixed loss for event i , we substitute the small co- efficient of variation, θ = 0 . 1, to give v < min$_{i}$ { 100 /x$_{i}$ } . We perform the minimisation over a set of 1001 equally-spaced values for v . Panjer recursion for random event losses. The Panjer algorithm needs each event loss to be a fixed (non-negative) integer. Therefore we follow the mixture approach of section 5 to replace an event i with a ran- dom loss with a collection of events with fixed losses. Consider event i , with loss distribution f$_{i}$ . We replace row i in the original ELT with n$_{q}$ rows each 32 v < min i { 1 θ $^{2}$x$_{i}$$^{}}$ .