Loss Models: From Data to Decisions, 4th Edition

8.4 Policy limits

The opposite of a deductible is a policy limit. The typical policy limit arises in a contract where for losses below u the insurance pays the full loss but for losses above u the insurance pays only u. The effect of the limit is to produce a right censored random variable. It will have a mixed distribution with distribution and density function given by (where Y is the random variable after the limit has been imposed)

and

The effect of inflation can be calculated as follows.

Theorem 8.6 For a policy limit of u, after uniform inflation of 1 + r, the expected cost is (1 + r)E[X Λ u/(1 + r)].

Proof: The expected cost is E(Y Λ u). The proof of Theorem 8.5 shows that this equals the expression given in this theorem.

For policy limits the concept of per payment and per loss is not relevant. All losses that produced payments prior to imposing the limit will produce payments after the limit is imposed.

EXAMPLE 8.6

Impose a limit of 3,000 on a Pareto distribution with α = 3 and θ = 2,000. Determine the expected cost per loss with the limit as well as the proportional reduction in expected cost. Repeat these calculations after 10% uniform inflation is applied.

For this Pareto ...