IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
In expected utility theory, an individual with a utility function U(w) is described as risk averse. Which property of U must hold for all levels of wealth w?
A risk-averse investor has a utility function with a positive first derivative, reflecting preference for more wealth, and a negative second derivative, reflecting diminishing marginal utility, which makes the function concave at every wealth level.
- AU'(w) > 0 and U''(w) < 0Correct
- BU'(w) > 0 and U''(w) > 0
- CU'(w) > 0 and U''(w) = 0
- DU'(w) < 0 and U''(w) < 0
- U'(w) = 0 and U''(w) < 0
Explanation
Non-satiation requires more wealth to be preferred, so U' > 0. Risk aversion requires a concave function, so U'' < 0. Option with U'' > 0 describes a risk seeker, and U'' = 0 describes risk neutrality.
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