IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
Which feature of a utility function U(w) implies that an investor is risk averse under expected utility theory?
Risk aversion corresponds to a utility function with a positive first derivative and a negative second derivative. The investor prefers more wealth, and concavity means the utility of expected wealth exceeds expected utility, so a certain outcome is preferred to a gamble.
- AU'(w) < 0 for all w
- BU''(w) > 0 for all w
- CU'(w) > 0 and U''(w) < 0 for all wCorrect
- DU'(w) > 0 and U''(w) > 0 for all w
- U''(w) = 0 for all w
Explanation
A positive first derivative means more wealth is preferred (non-satiation). A negative second derivative means concavity, so by Jensen's inequality E[U(W)] < U(E[W]) and the investor prefers certainty. U'' > 0 gives risk seeking and U'' = 0 gives risk neutrality.
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