Coverage Modifications: Inflation, Deductible Changes
Understand how inflation and deductible changes affect loss distributions and premiums for Exam STAM.
Impact of Inflation on Losses
Inflation uniformly scales all losses by a factor (1+r). For a policy with deductible d, inflation increases both the frequency of claims exceeding the deductible and the severity of those claims. The loss elimination ratio (LER) changes because the effective deductible in real terms decreases. If losses follow a Pareto distribution with parameters alpha and theta, inflated losses have theta replaced by theta(1+r). For policies with limits, inflation can push more losses against the policy limit, changing the expected cost per claim.
Deductible Changes
Changing the deductible affects the expected cost per loss and per payment. The expected cost per loss with deductible d equals E[X] minus E[X wedge d], where E[X wedge d] is the limited expected value. The expected cost per payment divides this by the probability of exceeding the deductible. Exam STAM problems often involve calculating the impact of a deductible change on pure premiums, requiring you to compute limited expected values for distributions like Pareto, exponential, and lognormal.