IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
An investor has utility U(w) = ln(w). She holds wealth that will be either Rs 40,000 or Rs 90,000 with equal probability. What is her certainty equivalent wealth?
The certainty equivalent is Rs 60,000. With log utility it equals the geometric mean of the outcomes, sqrt(40,000 x 90,000) = 60,000. It lies below the expected wealth of Rs 65,000 because the investor is risk averse.
- ARs 60,000Correct
- BRs 62,500
- CRs 65,000
- DRs 58,000
- Rs 66,000
Explanation
E[U] = 0.5 ln40000 + 0.5 ln90000 = 0.5 ln(3,600,000,000) = ln(sqrt(3.6e9)) = ln 60,000. So the certainty equivalent is Rs 60,000, the geometric mean. Rs 65,000 is the expected wealth, the mistake being to ignore risk aversion.
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