Work out policy limit effect instantly with clear inputs, formula shown and shareable results.
A policy limit caps the insurer's payment per claim. With exponential severities the limited expected value is μ(1 − e^(−L/μ)), which shows how quickly extra limit stops buying much expected cover once L is a few multiples of the mean.
Limited expected value
E[min(X,L)] = μ(1 - e^(-L/μ))
Because only the thin tail beyond the old limit is added. Increased limit factors rise steeply at first and then flatten.
Yes — with heavier-tailed severities than exponential, high limits cost considerably more than this model suggests.