ASTAM: Limited expected values measure the layer you actually pay
A limit and a deductible operate on the loss variable in different ways. Define the insurer payment explicitly. For an ordinary deductible d and payment limit u, Y=min((X−d)+,u), not min(X,u)−d in every case.
Worked example or practice scenario
For an exponential loss with mean 1,000, E[min(X,500)]=1,000(1−e^−.5)≈393.47. With deductible 200 and payment limit 500, expected payment is 1,000(e^−.2−e^−.7)≈322.15.
Try this next
Sketch the payment function across X<200, 200<X<700 and X>700. Use the survival-function integral to verify the expectation. Confirm whether a stated policy limit is a ground-up loss limit or a maximum insurer payment.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.
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