Question

8. Losses in a certain business follow an exponential distribution with mean 90. Currently polcies of 15%. Using educes the have no modifications. Next year, the company is expecting uniform inflation only an ordinary deductible, define a policy using the following modifications that r expected value of the per-loss random variable to the pre-inflation level.

Answer 1

The company is expecting uniform inflation of 15%, therefore the expected losses will also increase in the same proportion.

Expected losses in a certain business = E(X):

E(X) = 90

Hence, expected losses post-inflation = E(X1) = 90*1.15 = 103.5

Using an ordinary deductible in the policy, we want to reduce the expected value of the per-loss random variable back to the pre-inflation level which is 90.

Hence, we need to value the deductible as 103.5 - 90 = 13.5 ~ 14

Therefore, the policy should be modified as there should be a ordinary deductible of 14 losses to reduce the expected value of the per-loss random variable to the pre-inflation level.