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IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk

Which statement about the non-satiation and risk-aversion assumptions in utility theory is correct?

Non-satiation corresponds to a positive first derivative of utility, and risk aversion corresponds to a negative second derivative. The other options swap these conditions or wrongly claim risk-averse investors always reject risk or just minimise variance regardless of expected return.

  1. ANon-satiation means U''(w) < 0
  2. BRisk aversion means U'(w) > 0
  3. CA risk-averse investor always prefers the investment with the lower variance
  4. DNon-satiation means U'(w) > 0; risk aversion means U''(w) < 0Correct
  5. Risk aversion implies the investor rejects every risky investment

Explanation

Non-satiation means more wealth is preferred, so U' is positive. Risk aversion means diminishing marginal utility, so U'' is negative. A risk-averse investor still accepts risk if compensated by sufficient return, and does not choose on variance alone.

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