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

Ground-up losses are exponential with mean Rs 50,000. An insurer pays losses in excess of a deductible of Rs 20,000 (payment per payment). Next year, losses inflate by 20% and the deductible stays fixed. What is the expected payment per payment next year?

The expected payment per payment is Rs 60,000. Inflation raises the exponential mean from 50,000 to 60,000, and because the exponential distribution is memoryless, the average excess over the Rs 20,000 deductible, given a payment is made, equals the full mean.

  1. ARs 50,000
  2. BRs 60,000Correct
  3. CRs 72,000
  4. DRs 40,000
  5. Rs 80,000

Explanation

Inflated losses are exponential with mean 50,000 x 1.2 = 60,000. By the memoryless property, the expected excess over any deductible, given the loss exceeds it, equals the mean, 60,000. Using 50,000 ignores the inflation; 72,000 wrongly adds the deductible effect to the inflated mean.

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