Exam 8: A layer cost is a difference of limited expected values
For a layer of width u above attachment d, payment is min((X−d)+,u). Its expectation equals E[min(X,d+u)]−E[min(X,d)] under a nonnegative loss model. Ground-up, limited and excess data have different meanings.
Worked example or practice scenario
For a toy exponential loss with mean 1,000, a 500-wide layer above 500 has expected payment 1,000(e^−.5−e^−1)≈238.65. The expected payment is not simply 500 times the probability of exceeding 500 because some losses only partly use the layer.
Try this next
Draw the payment function and integrate the survival function across the layer. Then explain how censored policy-limit observations affect fitting the underlying severity distribution. State whether limits apply per claim, per occurrence or in aggregate.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.