IAI Actuarial Core Principles · Economic Modelling · Role of insurance in reducing or removing risk
A person has initial wealth of Rs 100 and utility U(w) = sqrt(w). With probability 0.5 she suffers a loss of Rs 36, otherwise no loss. What is the maximum premium she would pay for full insurance against this loss?
The maximum premium is Rs 19. Expected utility without cover is 9, which corresponds to certain wealth of Rs 81. Subtracting this from initial wealth of Rs 100 gives Rs 19, which exceeds the expected loss of Rs 18 because she is risk averse.
- ARs 16
- BRs 18
- CRs 19Correct
- DRs 20
- Rs 17
Explanation
Expected utility without insurance = 0.5*sqrt(100) + 0.5*sqrt(64) = 0.5*10 + 0.5*8 = 9. The certainty equivalent wealth is 9^2 = 81. Maximum premium = 100 - 81 = Rs 19. Rs 18 is the expected loss, which is the fair premium and not the maximum she would pay.
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