IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
An investor has utility U(w) = ln(w). She holds wealth of Rs 100,000 and is offered a gamble that gives an equal chance of ending wealth Rs 40,000 or Rs 250,000... Which is the certainty equivalent wealth of this gamble?
The certainty equivalent is Rs 100,000. With log utility it equals the geometric mean of the outcomes, the square root of 40,000 times 250,000, which is 100,000. The arithmetic mean of Rs 145,000 wrongly ignores risk aversion.
- ARs 100,000Correct
- BRs 145,000
- CRs 90,000
- DRs 120,000
- Rs 70,000
Explanation
E[ln W] = 0.5 ln(40,000) + 0.5 ln(250,000) = 0.5 ln(10,000,000,000) = ln(100,000). So the certainty equivalent is exp of that, Rs 100,000, the geometric mean. The arithmetic mean Rs 145,000 ignores risk aversion.
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