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

An individual has a strictly increasing, strictly concave utility of wealth function. Which of the following statements about this individual's attitude to a fair gamble is correct?

A person with strictly concave utility is risk averse. By Jensen's inequality the expected utility of a fair gamble is lower than the utility of its expected value, so she prefers receiving the expected value for certain and rejects the gamble.

  1. AShe is indifferent between the gamble and its expected value
  2. BShe would reject the gamble in favour of receiving its expected value for certainCorrect
  3. CShe would accept the gamble because expected utility rises with variance
  4. DShe would accept the gamble only if wealth is above a threshold
  5. Her preference depends only on the third derivative of utility

Explanation

By Jensen's inequality, for concave U, E[U(W)] < U(E[W]). So the individual prefers the certain expected wealth to the fair gamble, which is risk-averse behaviour. Indifference would require linear utility.

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