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IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility

An individual with a strictly concave, increasing utility function U(w) has wealth that is uncertain. Which statement about her behaviour under expected utility theory is correct?

She prefers the certain expected value to the gamble. With a concave utility function, Jensen's inequality gives E[U(W)] below U(E[W]), so the sure amount yields higher expected utility. This is the definition of risk aversion and underlies demand for insurance.

  1. AShe prefers the gamble to its expected value for certain
  2. BShe is indifferent between the gamble and its expected value for certain
  3. CShe prefers its expected value for certain to the gambleCorrect
  4. DShe values the gamble at more than its expected value
  5. Her marginal utility of wealth increases as wealth increases

Explanation

By Jensen's inequality, for concave U, E[U(W)] < U(E[W]). So a risk-averse person prefers the certain expected value to the gamble. Options suggesting preference for the gamble or increasing marginal utility describe risk-seeking behaviour or are inconsistent with concavity.

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