Thanks, that makes sense. So if you are at a multiple you have the probability of multiple losses hitting the size of the layer, and that causes a discontinuity?
Think about the number of ways you can make a multiple of the layer using claims from within the layer. In essence, if you try making a multiple using claims from lower down in the layer then you need more of them to reach the multiple. However, the expected number of claims is low, so that type of scenario is increasingly unlikely. Hence the jump discontinuities.
At larger multiples of the layer there are more ways to reach that aggregate claim total without needing as many claims, so the jump discontinuities become increasingly smaller.
Comments
This is the graph of the cumulative distribution function for aggregate claims, i.e. y = F_S(x) where x is the aggregate claim amount (total claim $).
Thanks, that makes sense. So if you are at a multiple you have the probability of multiple losses hitting the size of the layer, and that causes a discontinuity?
Think about the number of ways you can make a multiple of the layer using claims from within the layer. In essence, if you try making a multiple using claims from lower down in the layer then you need more of them to reach the multiple. However, the expected number of claims is low, so that type of scenario is increasingly unlikely. Hence the jump discontinuities.
At larger multiples of the layer there are more ways to reach that aggregate claim total without needing as many claims, so the jump discontinuities become increasingly smaller.
Thanks!