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IAI Actuarial Core Principles · Economic Modelling · Role of insurance in reducing or removing risk

An individual has initial wealth Rs 100 and utility U(w) = ln(w). She faces a 50% chance of losing Rs 36 (so wealth Rs 64) and a 50% chance of no loss. What is the maximum premium she would pay for full insurance (to the nearest rupee)?

The maximum premium is Rs 20. Expected utility equals ln of the geometric mean sqrt(100 x 64) = 80, so the certainty equivalent wealth is Rs 80, and she would pay up to 100 - 80 = Rs 20, exceeding the Rs 18 expected loss.

  1. ARs 18
  2. BRs 20Correct
  3. CRs 24
  4. DRs 36
  5. Rs 16

Explanation

E[U] = 0.5 ln100 + 0.5 ln64 = ln(sqrt(6400)) = ln80. Certainty equivalent wealth is 80, so the maximum premium is 100 - 80 = Rs 20. The expected loss is Rs 18, so Rs 18 is the fair premium, not her maximum.

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