IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
An individual with exponential utility U(w) = -exp(-0.01w) faces a loss that is normally distributed with mean Rs 0 change in wealth and variance 400 (in Rs squared) around initial wealth. Using the result that the certainty equivalent change is mean minus (a/2) times variance, with a the coefficient of absolute risk aversion, what is the maximum amount she would pay to remove this risk entirely?
The maximum amount is Rs 2. For exponential utility with normal outcomes, the risk premium equals half the absolute risk aversion coefficient times the variance: 0.5 × 0.01 × 400 = 2.
- ARs 0.5
- BRs 1
- CRs 2Correct
- DRs 4
- Rs 20
Explanation
Risk premium = (a/2) * variance = (0.01/2) * 400 = 2. Rs 4 would arise by omitting the one-half factor; Rs 20 arises from using the standard deviation instead of the variance.
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