Fall 2014 Q6.b
In sample solution 2, why are they not dividing by (1-F_x(A)) when getting E[500k xs 500k]? I would have thought we would need to based on this formula:
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This question is dealing with aggregate claims rather than just claim severity or claim frequency. Although we're given a severity trend of 20%, since the excess layer is fixed at 500k excess of 500k, there is an implicit frequency trend as well because more claims now trend into the layer.
The formula we want to use is E[S] = E{N_A] * E[X_A ; L] = (1 - F_X(A)) * E[N] * { (E[X;A+L] - E[X;A]) / (1 - F_X(A))} so the 1 - F_X(A) terms cancel out.