Loss Elimination Ratio (LER) is defined as which ratio?

• A. E[min(X, d)] / E[X]
• B. E[X] / E[min(X, d)]
• C. E[max(X, d)] / E[X]
• D. E[d] / E[X]

Answer: (A)

The main idea is how much of the potential loss is kept when payments are capped at a limit d. If a loss X occurs and payments are limited to d, the amount actually paid is min(X, d). The Loss Elimination Ratio captures what fraction of the original expected loss remains after applying that cap, which is the expected payout under the cap divided by the expected original loss: E[min(X, d)] / E[X].

This is why the first option is correct. It directly computes the portion of the expected loss that survives the cap. For intuition, if d is very large, min(X, d) tends to X and the ratio approaches 1, meaning almost all expected loss is retained. If d is small relative to typical X, the ratio drops, reflecting more loss being eliminated by the cap.

The other choices don’t fit this concept. Taking the reciprocal would describe the inverse relationship, not the retained fraction. Using the maximum, E[max(X, d)] / E[X], would describe a quantity tied to the larger of X and d, not the retained loss under a cap. Using E[d] ignores the randomness of X altogether and doesn't measure how much of the actual loss is retained.