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

A general insurer's motor policy has an ordinary (non-franchise) deductible of Rs 20,000 per loss. A loss of Rs 55,000 occurs. Which statement describes the insurer's payment and the insured's retained amount?

The insurer pays Rs 35,000 and the insured keeps Rs 20,000. An ordinary deductible is subtracted from every loss that exceeds it, so the insurer pays the loss minus the deductible, while the policyholder bears the first Rs 20,000.

  1. AInsurer pays Rs 55,000; insured retains nothing
  2. BInsurer pays Rs 35,000; insured retains Rs 20,000Correct
  3. CInsurer pays Rs 20,000; insured retains Rs 35,000
  4. DInsurer pays Rs 75,000; insured retains Rs 20,000
  5. Insurer pays Rs 35,000; insured retains Rs 55,000

Explanation

With an ordinary deductible d, the insurer pays max(X - d, 0) = 55,000 - 20,000 = 35,000. The insured bears the first 20,000. Option 0 describes a franchise deductible that has been exceeded, which is a different arrangement.

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