Loss Models: From Data to Decisions, 4th Edition

8.3 The loss elimination ratio and the effect of inflation for ordinary deductibles

A ratio that can be meaningful in evaluating the impact of a deductible is the loss elimination ratio.

Definition 8.4 The loss elimination ratio is the ratio of the decrease in the expected payment with an ordinary deductible to the expected payment without the deductible.

While many types of coverage modifications can decrease the expected payment, the term loss elimination ratio is reserved for the effect of changing the deductible. Without the deductible, the expected payment is E(X). With the deductible, the expected payment (from Theorem 8.3) is E(X) − E(X Λ d). Therefore, the loss elimination ratio is

provided E(X) exists.

EXAMPLE 8.4

Determine the loss elimination ratio for the Pareto distribution with α = 3 and θ = 2.000 with an ordinary deductible of 500.

From Example 8.3, we have a loss elimination ratio of 360/1,000 = 0.36. Thus 36% of losses can be eliminated by introducing an ordinary deductible of 500.

Inflation increases costs, but it turns out that when there is a deductible, the effect of inflation is magnified. First, some events that formerly produced losses below the deductible will now lead to payments. Second, the relative effect of inflation is magnified because the deductible ...