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

Which statement about the von Neumann-Morgenstern axioms and expected utility is correct?

Expected utility rankings are unchanged by a positive linear transformation of the utility function, so utility is unique only up to scale and origin. The axioms do not force risk neutrality or concavity; those reflect individual risk attitudes.

  1. AUtility functions are unique, so any change in scale alters the ranking of gambles
  2. BPreferences consistent with the axioms are unchanged by a positive linear transformation of the utility functionCorrect
  3. CExpected utility requires every investor to be risk neutral
  4. DCompleteness means an investor must prefer riskier gambles
  5. Transitivity implies utility must be a concave function

Explanation

Expected utility rankings are preserved under U* = aU + b with a > 0, so utility is defined only up to a positive linear transformation. The other statements confuse axioms with risk attitudes; concavity reflects risk aversion, not transitivity.

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