Skip to content

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

A policyholder with utility U(w)=ln(w) has wealth of Rs 100,000 and faces a 10% chance of losing Rs 60,000 and a 90% chance of no loss. Which statement is correct about the maximum premium she would pay for full cover?

The maximum premium exceeds the expected loss of Rs 6,000. Log utility is concave, so the uninsured gamble has lower expected utility than its expected wealth of Rs 94,000, and she will pay a risk premium on top of the expected loss, about Rs 11,000 here.

  1. AExactly Rs 6,000, the expected loss, because she is risk averse
  2. BLess than Rs 6,000, because she is risk averse
  3. CMore than Rs 6,000, because expected utility of the uninsured position is below utility of wealth less expected lossCorrect
  4. DExactly Rs 60,000, the size of the loss
  5. Zero, because log utility implies risk neutrality

Explanation

Log utility is concave, so by Jensen the expected utility of the gamble is below the utility of its expected wealth (Rs 94,000). Hence the certainty equivalent is below 94,000 and the maximum premium exceeds the expected loss of Rs 6,000. Check: 0.1 ln40000+0.9 ln100000 = 11.4876, giving a certainty equivalent of about Rs 89,000 and a maximum premium of about Rs 11,000.

Did you get it right without looking?

One question tells you little. A timed set on Role of insurance in reducing or removing risk shows your real accuracy, how long you take and where you lose marks.

Practise Role of insurance in reducing or removing riskFree diagnostic mock

More Role of insurance in reducing or removing risk questions