Skip to content

IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing

Which statement about an ordinary deductible d applied to ground-up loss X is correct?

The expected payment per payment equals the expected payment per loss divided by the probability that the loss exceeds the deductible. Per loss figures include zero payments, so they are lower than per payment figures whenever some losses fall below the deductible.

  1. AThe expected payment per loss equals the expected payment per payment.
  2. BThe expected payment per payment equals the expected payment per loss divided by P(X > d).Correct
  3. CThe expected payment per loss exceeds the expected payment per payment whenever P(X > d) < 1.
  4. DThe deductible does not change the variance of the insurer's payment per loss.
  5. A franchise deductible pays X − d when X exceeds d.

Explanation

Per loss payment is (X−d)+, which is zero with probability P(X≤d). Per payment conditions on X>d, so E[per payment] = E[(X−d)+]/P(X>d). Since the divisor is below 1, per payment is the larger, which rules out the third option. A franchise deductible pays the full X once X exceeds d.

Did you get it right without looking?

One question tells you little. A timed set on Loss distributions, with and without risk sharing shows your real accuracy, how long you take and where you lose marks.

Practise Loss distributions, with and without risk sharingFree diagnostic mock

More Loss distributions, with and without risk sharing questions