To derive the expected loss cost to an XL layer (formula 2.3) there is a step from: E[N] E[{X - D /\ L} \/ 0] to E[N] E[X /\ (L+D) - X /\ D] I understand what the first line is saying i.e. the expected frequency times the expected severity less the deductive which is overall limited to L.... ...but not how this is equal to the second line or even what the second is saying? Thanks
X /\ (L+D) - this is the claim amount X with an upper limit of the deductible D and the layer width L X /\ D - this is the claim amount X with an upper limit of the deductible D If X < D, E[X /\ (L+D) - X /\ D] = E[X -X] = 0 = zero layer cost If X > L+D, E[X /\ (L+D) - X /\ D] = E[L+D -D] = L = maximum layer cost If D < X < L+D, E[X /\ (L+D) - X /\ D] = E[X -D] = claim minus deductible hope this helps Dan
