Skip to content

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

An individual with a strictly concave utility function of wealth is offered full insurance against a random loss at a premium equal to the expected loss. Which statement is correct?

She prefers to insure. With concave utility she is risk averse, so by Jensen's inequality the utility of certain wealth equal to expected wealth exceeds the expected utility of the risky wealth. A fair-premium full cover therefore raises her expected utility.

  1. AShe is indifferent between insuring and not insuring, because the expected wealth is the same
  2. BShe prefers to insure, because the certain wealth gives higher expected utility than the uncertain wealthCorrect
  3. CShe prefers not to insure, because the premium reduces her expected wealth
  4. DShe prefers to insure only if her utility function is linear
  5. She prefers not to insure, because concave utility implies risk-seeking behaviour

Explanation

Under a concave utility function the individual is risk averse. By Jensen's inequality, U(E[W]) > E[U(W)]. Full insurance at the actuarially fair premium gives certain wealth equal to E[W], so expected utility is higher. Indifference arises only for linear utility (risk neutrality).

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