IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
Which statement about a risk-averse investor under expected utility theory is correct?
A risk-averse investor has a concave utility function, with diminishing marginal utility. By Jensen's inequality, expected utility of a non-degenerate gamble is lower than the utility of its expected value, so she values certainty over the gamble.
- AHer utility function is convex
- BHer utility function is linear in wealth
- CHer marginal utility of wealth is increasing in wealth
- DHer utility function is concave, so E[U(W)] is less than U(E[W]) for a non-degenerate gambleCorrect
- She will always prefer the prospect with higher variance
Explanation
Risk aversion corresponds to U'' < 0, i.e. concavity. Jensen's inequality then gives E[U(W)] < U(E[W]) for any non-degenerate gamble. Convex or linear utility describes risk-seeking or risk-neutral behaviour.
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