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IAI Actuarial Core Principles · Business Management · Decision-making process, attitude to risk and competition

In expected utility theory, an individual's utility of wealth function is concave, as is typical for a risk-averse person. Which of the following statements follows from this concavity?

A person with a concave utility function would pay more than the expected loss to insure against a random loss. Concavity means the utility of expected wealth exceeds expected utility, so removing uncertainty is worth a premium above the actuarially fair price.

  1. AMarginal utility of wealth rises as wealth rises
  2. BThe individual would pay more than the expected loss to insure against a random lossCorrect
  3. CThe individual is indifferent between a certain sum and a gamble with the same mean
  4. DThe individual would refuse any actuarially fair insurance cover
  5. The utility of the expected wealth is lower than the expected utility of wealth

Explanation

For a concave utility function, Jensen's inequality gives U(E[W]) > E[U(W)]. So the person values certainty more than the gamble and will pay a premium above the expected loss to remove the risk. Option 4 is reversed. Option 0 describes a convex function.

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