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

An insurer has an excess-of-loss reinsurance treaty with a fixed retention of Rs 50,000. Claims inflate by 8% a year with no change to the retention. Which statement about the effect on the insurer and reinsurer is correct?

The reinsurer's expected payments rise by more than 8%. With a fixed retention, inflation both brings more claims above the retention and enlarges the excess on claims already above it, so the layer is geared to inflation.

  1. AThe reinsurer's expected payments rise by less than 8%
  2. BThe reinsurer's expected payments rise by exactly 8%
  3. CThe reinsurer's expected payments rise by more than 8%Correct
  4. DThe insurer's retained claims rise by more than 8%
  5. Neither party is affected, since the retention is fixed

Explanation

With a fixed retention, inflation pushes more claims over the limit and increases the excess portion of those already over it. The reinsurer's layer therefore grows by more than the inflation rate (leveraging effect). Capped insurer payments then grow by less than 8%.

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